Denoising through wavelet shrinkage--an empirical study
Denoising through wavelet shrinkage:an
empirical study
Imola K.Fodor
Chandrika Kamath
Lawrence Livermore National Laboratory
Center for Applied Scienti?c Computing
P.O.Box808,L-560,Livermore,California94551
E-mail:fodor1@https://www.sodocs.net/doc/e39213958.html, and kamath2@https://www.sodocs.net/doc/e39213958.html,
Abstract.Techniques based on thresholding of wavelet coef?cients are gaining popularity for denoising data.The idea is to transform the data into the wavelet basis,where the‘‘large’’coef?cients are mainly the signal,and the‘‘smaller’’ones represent the noise.By suitably modifying these coef?cients,the noise can be removed from the data.We evaluate several2-D denoising procedures using test images corrupted with additive Gaussian noise.We consider global,level-dependent,and subband-dependent implementations of these techniques.Our results,using the mean squared error as a measure of the quality of denoising,show that the SureShrink and the BayesShrink methods consistently outperform the other wavelet-based techniques.In contrast,we found that a combination of simple spatial?lters lead to images that were grainier with smoother edges,though the error was smaller than in the wavelet-based methods.?2003SPIE and IS&T.[DOI:10.1117/1.1525793]
1Introduction
With sensors becoming ubiquitous and computers becom-ing more powerful,scientists are collecting and analyzing data at an ever-increasing pace.In many?elds such as as-tronomy,medical imaging,and computer vision,the data that is collected is often noisy,either as a result of the data acquisition process or due to natural phenomena such as atmospheric disturbances.This noise must be removed be-fore the data can be analyzed.
Removing the noise from data can be considered as the process of constructing optimal estimates of the unknown signal from the available noisy data.There are several dif-ferent ways in which this denoising can be done.In this paper,we investigate wavelet-based techniques for denois-ing,focusing on shrinkage methods.The basic idea behind these techniques is to use wavelets to transform the data into a different basis,where‘‘large’’coef?cients corre-spond to the signal,while‘‘small’’ones represent mostly noise.The wavelet coef?cients are suitably modi?ed and the denoised data is obtained by applying an inverse wave-let transform to the modi?ed coef?cients.
In our work,we consider2-D versions of methods that were originally developed for1-D signals in Refs.1through5and compare them to the method proposed for images in https://www.sodocs.net/doc/e39213958.html,ing decimated wavelet transforms,and the mean squared error optimality criterion,we evaluate the different methods on test images corrupted with additive Gaussian white noise.Our goal is to address several issues. First,we want to better understand the sensitivity of the different methods to the choice of wavelet?lters,the num-ber of multiresolution levels,and the values of the param-eters in each method.Second,we want to identify tech-niques that perform well across a variety of images and noise levels.Third,in contrast with other work,we want to explore the effect of different ways of modifying the wave-let coef?cients for each method.By calculating and apply-ing the modi?cations either globally,in a level-dependent manner,or in a subband-dependent manner,we hope to ?ne-tune the wavelet denoising to an image.Finally,we want to compare and contrast these wavelet-based tech-niques with the more traditional approaches based on spa-tial?lters.Our goal is to complement the extensive theo-retical and algorithmic work presented in the literature with a more practical,implementation-oriented comparison that would guide a practitioner in the choice of a method.
This paper is organized as follows.Section2gives a brief introduction to various denoising methods,followed by a detailed description of denoising through the shrinkage of wavelet coef?cients.We describe the options available for such techniques and the different methods used to implement each option.Section3reports the results of the wavelet-based denoisers on test images with varying levels of additive white Gaussian noise.Section4compares the wavelet-based techniques to the more traditional ap-proaches to denoising based on spatial?lters.Finally,Sec. 5concludes with a summary and possible extensions.
2Techniques for Removing Noise from Data Spatial?lters have long been used as the traditional means of removing noise from images and signals.7These?lters usually smooth the data to reduce the noise,but in the process,also blur the data.In the last decade,several new techniques have been developed that improve on spatial ?lters by removing the noise more effectively while pre-serving the edges in the data.Some of these techniques borrow ideas from partial differential equations and com-
Paper JEI01048received Jul.30,2001;revised manuscript received Mar.26,2002
and Aug.14,2002;accepted for publication Aug.14,2002.
1017-9909/2003/$15.00?2003SPIE and IS&T.
Journal of Electronic Imaging12(1),151–160(January2003).
Journal of Electronic Imaging/January2003/Vol.12(1)/151
putational?uid dynamics such as level set methods,8,9total variation methods,10,11nonlinear isotropic and anisotropic diffusion,12,13and essentially nonoscillatory?ENO?schemes.14Other techniques combine impulse removal?l-ters with local adaptive?ltering in the transform domain to remove not only white and impulsive noise,but also their mixtures.15A different class of methods exploits the de-composition of the data into the wavelet basis and shrinks the wavelet coef?cients to denoise the data.1–6,16,17While this is typically done using the more memory ef?cient deci-mated wavelet transforms,it is well known that the use of nondecimated transforms minimizes the artifacts in the de-noised data.18,19Other authors have combined wavelets with hidden Markov models and spatially adaptive methods,20–26or used other basis functions such as ridge-lets and curvelets27,28that can be more effective than wave-lets for images and higher dimensional data.
All these,and other,techniques have made image de-noising a very active research area.However,what is lack-ing is a thorough comparison of the advantages and disad-
vantages of the different methods.The absence of such investigations,even within a single class of techniques, makes it very dif?cult for a practitioner to select an appro-priate denoising scheme from the wealth of techniques that have been proposed in the literature.Our goal in this paper is to address this drawback in a small way by comparing and contrasting several of the different denoising methods that are based on the shrinkage of wavelet coef?cients. 2.1Denoising by Wavelet Shrinkage
The problem of denoising data can be stated as follows: given the zero-mean observation data Y i,j as a noisy real-ization of the signal X i,j,
Y i,j?X i,j??i,j,i?1,...,I,j?1,...,J,?i,j?N?0,?2?,
?1?
construct an‘‘optimal’’estimate X?i,j of X i,j based on Y i,j. In this paper,we assume that the??i,j?s are independent from the signal and are independent and identically distrib-uted Gaussian?normal?random variables with mean zero and variance?2.We also use the minimal mean squared error?MSE?to evaluate the optimality of the estimates.Let Y,X,and?denote the observed data,the noiseless data, and the error matrices in Eq.?1?,respectively.Then,the three main steps of denoising using the wavelet coef?cient shrinkage technique are as follows:
1.Calculate the wavelet coef?cient matrix w by apply-
ing a wavelet transform W to the data:
w?WY?WX?W?,?2?
2.Modify?i.e.threshold or shrink?the detail coef?-
cients of w to obtain the estimate w?of the wavelet
coef?cients of X:
w→w?,?3?
3.Inverse transform the modi?ed coef?cients to obtain
the denoised estimate:
X??W?1w?.?4?
The number N of the wavelet coef?cients w in Eq.?2?varies depending on the type of transform used.We focus on decimated transforms,29where N?IJ,regardless of the number of multiresolution levels K,as it requires less memory than the undecimated transform.Figure1displays the subbands of a two-level(K?2)decimated decomposi-tion.The coef?cients on the?rst level are grouped into the vertical detail(LH1),horizontal detail(HL1),diagonal de-tail(HH1),and smooth(LL1)subbands.The smooth part is then similarly decomposed into the four second level subbands.The directions re?ect the order in which the high-pass?H?and low-pass?L??lters of the wavelet trans-form are applied along the two dimensions of the original image.
The?rst step in denoising is to select a wavelet for the forward and inverse transformations W and W?1in Eqs.?2?and?4?,respectively.We investigate well-known or-
thogonal and biorthogonal wavelets including the Daubechies family?daublets?,the least asymmetric wavelet family?symmlets?,the coi?et family?coi?ets?,and the B-spline and V-spline families.30These wavelets differ in their support,symmetry,and number of vanishing mo-ments.In addition to a wavelet,we must also select the number of multiresolution levels and an option for handling values near the edges of the image.We consider several boundary treatment rules,31including periodic,symmetric, re?ective,constant,and zero-padding.
The remainder of this section explains the details in the shrinkage?sometimes called thresholding?step in Eq.?3?. Let w denote a single detail coef?cient and w?its shrunk ?thresholded?version.Let?be the threshold,??()denote the shrinkage function that determines how the threshold is applied to the data,and??be an estimate of the standard deviation?of the noise in Eq.?1?.Then,
w???????w/???,?5?or
w?????w?,?6
?Fig.1Wavelet decomposition subbands using a decimated trans-form with two multiresolution levels.
Fodor and Kamath 152/Journal of Electronic Imaging/January2003/Vol.12(1)
depending on whether the threshold?was determined as-suming a unit noise scale??1,in which case Eq.?5?ap-plies,or an estimation of the actual noise was built-in into the method,in which Eq.?6?would be appropriate.Note that the noise estimate,the threshold,and the shrinkage function could depend on either the multiresolution level or the subband,though we have suppressed this dependence in our notation.
The denoising methods we consider differ in the choices for???,?,and??,in Eqs.?5?and?6?.That is,we can obtain different denoisers by considering different
1.shrinkage functions that determine how the threshold
is applied?Sec.2.2?
2.noise estimates?Sec.2.3?
3.shrinkage rules to determine the threshold??Sec.
2.4?
Since certain shrinkage rules depend on the shrinkage func-tion and the noise estimate,we must?rst select???and??before we calculate?.
For1-D data,we can calculate the thresholds either glo-bally,with one threshold for all the coef?cients,or on a level-dependent basis,with K different thresholds for the K different dyadic levels.In two dimensions,in addition to these two possibilities,we can also calculate thresholds in a subband-dependent manner,and obtain3K thresholds for the3K detail coef?cient subbands.While typical publica-tions on denoising images6,10consider either the level-dependent or the subband-dependent alternative in addition to the global implementation,we consider all the three dif-ferent options.Next,we describe the different ways in which we can select the shrinkage functions,estimate the noise,and select the rules for denoising.More details can be found in Ref.32,which is available online.
2.2Shrinkage Functions
The shrinkage?thresholding?function determines how the thresholds are applied to the data.Figure2displays the four thresholding functions we studied,scaled to the interval ??1,1?.The x axis represents detail wavelet coef?cients w in Eq.?2?,and the y axis shows the corresponding thresh-olding function??(w).The dotted vertical lines indicate the values of the single threshold??for the hard???H(w)?, soft???S(w)?,and garrote???G(w)?functions.The semisoft
function??
1,?2
SS(w)requires two thresholds,??
1
and ??2,represented by the four dotted vertical lines in its graph.If I?a?denotes the?0,1?indicator function,corre-sponding to?a?False,a?True?,the mathematical expres-sions for each of the shrinkage functions are
??H?w??wI??w????,?7???S?w??sgn?w???w????I??w????,?8???G?w???w??2w?I??w????,?9?and ??
1
,?2
SS?w???0,?w?р?1
sgn?w?
?2??w???1?
?2??1,?1
??w?р?2 w,?w???2?.?10?
2.3Noise Estimates
Certain thresholds,as described in Sec.2.4,are determined assuming a unit noise scale,??1.Therefore,in practice, the data must be standardized by an estimate of the noise scale??according to Eq.?5?before applying these thresh-olds.In some cases,there is prior knowledge about the noise distribution that can be used to obtain?.However,in many situations,the noise must be estimated from the ob-served data.The options for estimating the noise scale in-clude the choice of the functional form of the estimator and the choice of the detail coef?cients to include in the esti-mation.We consider different estimation functions,includ-ing the sample standard deviation and the more robust scaled median absolute deviation?MAD?de?ned as???1/0.6745median??x i?:i?1,...,p?,given the realizations x1,...,x p from an independent identically distributed?i.i.d.?N(0,?2)process.1We also consider noise estimates that are global,level-dependent,or subband-dependent.
2.4Shrinkage Rules
The shrinkage?thresholding?rules determine how the thresholds are calculated.Let?denote a threshold.For convenience,the possible dependence of?on the multi-resolution level?k:1рkрK?or on the subband?s:1рs р3K?is suppressed in the notation.Certain rules calculate the threshold independent of the shrinkage function,while others obtain different thresholds for different
shrinkage
Fig.2Shrinkage functions.
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functions.In addition,certain rules assume a unit noise scale,??1;others do not.We indicate the assumptions of each method as we describe them here.
2.4.1Universal
The universal rule was proposed in Ref.2as a global rule for1-D signals.Regardless of the shrinkage function,for a signal of size N from a standard normal distribution N(0,1),the threshold is??(2log N)1/2.With a noise esti-
mate??,it is applied according to Eq.?5?.
2.4.2Minimizing the false discovery rate Introduced in Ref.5for1-D data,the minFDR rule deter-mines the same global threshold for all shrinkage functions by keeping the expected value of the fraction of coef?cients erroneously included in the reconstruction below a given fraction q.Given the N wavelet coef?cients w n,?rst it computes the p values:
p n?2?1????w n?/????,1рnрN,?11?where???is the cumulative distribution function of the standard normal distribution,and??is an estimate of the noise standard deviation.Then,it orders the p n values as p?1?рp?2?рˉрp?N?.?12?Starting with n?1,let m be the largest index n such that
p?n?рn
N
q.?13?
The threshold is then obtained as
??????1?1?p?m?2?.?14?
As??is already factored in,the threshold is applied accord-ing to Eq.?6?.
2.4.3Top
The top rule for1-D signals3is a global method,indepen-dent of the shrinkage function.Given p as the fraction of the largest coef?cients to keep,the threshold?is set to be the(1?p)’th quantile of the empirical distribution of the absolute values of the wavelet coef?cients.It is applied to the coef?cients using Eq.?6?.
2.4.4SURE
For1-D data,thresholds derived by minimizing Stein’s un-biased risk estimate?SURE?depend on the shrinkage func-tion and on the multiresolution level.1The generalization to images can be achieved in either level-or subband-dependent manners.In the latter case,the threshold on sub-band s is
?s?arg min
?у0SURE??,w s?,?15?
where w s denotes the detail coef?cients from subband s,
and SURE(?,w s)denotes the corresponding Stein’s unbi-
ased estimate of the risk corresponding to a speci?c shrink-
age function.For example,the threshold on subband s to be
used with the soft shrinkage function?s S is chosen as the
value that minimizes SURE S(?,w s),
?s S?arg min
?у0
SURE S??,w s?,?16?
where
SURE S??,w s??N s??n?1
N s
?min??w n?,???2
?2??#of w n?:?w n?р??,?17?
and N s1,32is the number of coef?cients w n in w s.The
preceding threshold assumes??1.For data with nonunit
variance,the coef?cients are standardized by an appropriate
??estimate before calculating the threshold with Eq.?16?.
The level-dependent implementation is similar,except that
instead of using the coef?cients on a subband,one uses the
coef?cients on a level.
It was shown in Ref.1that,in the case where the wave-
let coef?cient decomposition is sparse,a hybrid method
combining the universal and the SURE thresholds is pref-
erable over SURE.This hybrid method,when combined
with the soft shrinkage function is referred to as SureShrink
in the literature.1If
1
N s
?
n?1
N s??w n???2?1?р?log2N s?3/2?N s,?18?
then SureShrink uses the universal threshold,otherwise the
SURE threshold is used for the coef?cients on subband s.
Thresholds for the other shrinkage functions can also be
derived.We worked out the details for hard thresholding,
but in reporting the results,we simply call it SURE thresh-
olding with hard shrinkage,instead of WaveChop,as sug-
gested in Ref.1.
2.4.5Hypothesis testing
Introduced in Ref.4for1-D signals,the hypTest rule cal-
culates level-dependent thresholds independent of the
thresholding function,based on testing the hypothesis that
the wavelet coef?cients at a given level are zero.In our
extension to images,we distinguish between the level-
dependent and the subband-dependent implementations.
Following the notation in the description of the SURE
rule for the subband-dependent version,and assuming that
the N s wavelet coef?cients on subband s are normally dis-
tributed,we?rst?nd the largest of the squared wavelet
coef?cients on the subband,denoted by w(N
s)
2,then com-
pare it to the critical value
c N
s
?????1?1
2??1?
??1/N s?1???2,?19?
Fodor and Kamath
154/Journal of Electronic Imaging/January2003/Vol.12(1)
where ?is the predetermined Type I error probability in the testing and ???is the cumulative distribution function of the standard normal density.If
w ?N s ?
2??
2
?c N s
?
,
?20?
where ?
?is an estimate of the standard deviation of the noise,the null hypothesis of zero mean associated with the largest ?in absolute value ?coef?cient is rejected,and so w (N s )is retained as signal.Next,the process is iterated with the square of the second largest ?in absolute value ?wavelet
coef?cient w (N s ?1)2.If w (N s ?1)2/?
?2?c N s
?1?
,the procedure continues until at some point the m ’th largest ?in absolute value ?coef?cient satis?es
w ?m ?
2??
2
рc m ?
.
?21?
The threshold at subband s is then set as ?s ??w ?m ??,
?22?
and is applied according to Eq.?6?.
2.4.6BayesShrink
The BayesShrink rule of Ref.6uses a Bayesian mathemati-cal framework for images to derive subband-dependent thresholds that are nearly optimal for soft thresholding.The formula for the threshold on a given subband s is
?s ???2??X
,
?23?
where ?
?2is the estimated noise variance,and ??X 2
is the estimated signal variance on the subband considered.The noise variance is estimated as the scaled median absolute deviation of the diagonal detail coef?cients on level 1?i.e.,subband HH 1).The estimate of the signal standard devia-tion is
??X ??max ???Y 2??
?2,0??1/2,?24?
where
??Y 2?1N s ?
n ?1N
s w n
2
,
?25?
is an estimate of the variance of the observations,with N s being the number of the wavelet coef?cients w n on the
subband under consideration.In the case when ??2у??Y 2,the
threshold is set to ?s ?max(?w n ?),and all coef?cients from the subband are set to zero.These thresholds are applied according to Eq.?6?.
This method has been proposed for use with soft thresh-olding.We use the thresholds calculated via this procedure with other thresholding functions as well,but,in compli-ance with Ref.6,we reserve the term BayesShrink for de-noising with the soft shrinkage function.
It is clear from the description of the various shrinkage rules,that some of them depend on parameters.We next describe our experimental results,including the empirical determination of the values of these parameters.
3Experimental Results
We compared the various denoising methods described in Section 2on several test images widely used in the image processing community.Here,we report the results only for the Lena https://www.sodocs.net/doc/e39213958.html,plete results for other test images can be found in Ref.32.Our experimental approach was as follows.First,we obtained the 512-?512-pixel,noiseless,gray-scale originals from https://www.sodocs.net/doc/e39213958.html,.hk/imagedb/.We corrupted these images by adding Gaussian noise to the images according to Eq.?1?,using ??10,20,and 30.Figure 3?a ?shows the original ‘‘Lena’’image and Fig.3?b ?shows the image with additive Gaussian noise with ??20.Next,we determined the parameters for the shrinkage rules,as described in https://www.sodocs.net/doc/e39213958.html,ing these pa-rameters,we applied the wavelet denoising methods,each in a global,level-dependent,and subband-dependent man-ners.We evaluated the quality of the denoising using the
MSE,de?ned for a given estimate X
?(i ,j )of X (i ,j )
as Fig.3Denoising results for the ‘‘Lena’’image:(a)original image;(b)noisy image,??20,MSE ?399.50;(c)SureShrink and MSE ?61.59;(d)global universal rule with hard thresholding and MSE ?103.95;(e)minimum MSE (5?5)followed by Gaussian (3?3)?lter,MSE ?56.80;(f)minimum MSE (5?5)followed by mean (3?3)?lter,MSE ?64.80.
Denoising through wavelet shrinkage ...
Journal of Electronic Imaging /January 2003/Vol.12(1)/155
MSE?X,X???1
IJ
?
i?1
I
?
j?1
J
?X?i,j??X??i,j??2.?26?
3.1Selection of Parameters
We determined the‘‘optimal’’parameters for the minFDR, top,and hypTest denoising methods empirically,using the 512-?512-pixel gray-scale‘‘Lena’’test image with addi-tive Gaussian noise with??10,the symmlet8wavelet, four multiresolution levels and periodic boundary treatment.32We chose the symmlet8wavelet as it is rela-tively symmetric,and has a reasonably compact support.
For the minFDR rule,we found the optimal parameters to be q?0.2for the global implementation,and q?0.3for the level and the subband-dependent implementations.The global implementation was superior to the level-dependent one,which,in turn,was superior to the subband-dependent version.
For the top procedure,we determined the best parameter as p?0.3for the global implementation,and as p1?0.15, p2?0.4,p3?0.8,and p4?0.95on multiresolution levels1 through4,respectively,for the level-dependent and the subband-dependent cases.The level-dependent method was the best,followed by the subband-dependent,followed by the global implementation.For the top rule with the semi-soft shrinkage function,we calculated the thresholds by using two different p parameters.The optimal parameter pair for the global implementation was?p1?0.1,p2?0.01?.We obtained the best subband and level-dependent results with?p1(1)?0.15,p2(1)?0.1?,?p1(2)?0.3,p2(2)?0.1?,?p1(3)?0.6,p2(3)?0.2?,?p1(4)?0.7,p2(4)?0.3?,where the su-perscripts indicate the multiresolution levels.The global implementation was the best,the subband-dependent was second,and the level-dependent was third.
For the hypTest rule,in agreement with Ref.33,we found an unusually high value,??0.9,to be optimal.The subband-dependent implementation outperformed the level-dependent version,which outperformed the global one.
For the methods that required an estimate of?,we used the scaled MAD of the detail coef?cients on the HH1 subband,1as it was the most robust among the alternatives we tried.A typical such estimate for??10is???10.52.
3.2Comparison of Wavelet-Based Techniques Table1presents the results of denoising for the‘‘Lena’’image.The three main columns report the MSE values cor-responding to the three different noise levels.The?rst row contains the MSEs for the noisy images,enabling evalua-
tion of the denoised results.The thresholding rules are pre-?xed with either S–or P–to indicate whether the thresh-olds were calculated globally?i.e.,single threshold?,or dependent on the level or subband?i.e.,pyramid of thresh-olds?.For all methods,we considered both level-and subband-dependent implementations,but report only the better of the two approaches for each method.The bold-faced entry in each column indicates the best method for the corresponding noise level.Figure3displays a few ex-amples of the denoised results.
As seen from Table1,the quality of the denoised images varies greatly.For example,for the??20image,although all methods decrease the MSE?399.50of the noisy image, the denoised MSE values range from the worst of351.63to the best of61.59.The choice of the method therefore strongly in?uences the results.
We next summarize our observations based on the ex-perimental results reported here,and in a more detailed study.32Except for the different quantities involved,the main conclusions reached for the‘‘Lena’’image are valid for the other images included in Ref.32.In the following, recall that SureShrink and BayesShrink refer to subband-dependent soft shrinkage with the P–SURE and P–Bayes rules,respectively.
Table1Wavelet-based MSE results for the‘‘Lena’’image,the sym-mlet12wavelet,three multiresolution levels,and periodic boundary treatment.
Rule??10??20??30 Noisy Image99.53399.50894.66 Soft S–Universal86.57136.52169.40
S–MinFDR33.2681.13143.89
S–Top33.3591.46177.24
S–HypTest33.50103.12261.45
S–SURE33.7074.91113.01
S–Bayes39.0975.77115.18
P–Universal76.45123.54156.90
P–MinFDR33.5981.80143.74
P–Top29.9275.06141.46
P–HypTest31.83112.41292.43
P–SURE29.2361.5991.34
P–Bayes30.2663.3392.74 Hard S–Universal55.98103.95142.44
S–MinFDR75.40282.55622.14
S–Top80.20317.27709.56
S–HypTest72.39339.18810.56
S–SURE70.23257.76562.66
S–Bayes92.38240.58255.64
P–Universal49.5593.58128.61
P–MinFDR75.11280.66618.50
P–Top68.56263.28584.97
P–HypTest76.71351.63829.56
P–SURE70.24257.81561.53
P–Bayes48.26101.29152.54 Garrote S–Universal69.81121.28158.12
S–MinFDR37.70115.52234.12
S–Top41.09143.96311.00
S–HypTest36.12169.95463.92
S–Bayes58.0193.61112.14
P–Universal60.98107.77143.52
P–MinFDR37.60114.75231.91
P–Top34.79111.59234.01
P–HypTest38.36190.23511.85
P–Bayes34.3771.35103.66 SemiSoft S–Top33.0991.46200.92
P–Top56.95214.62475.91
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3.2.1In?uence of shrinkage function
As the values in Table1indicate,in most cases,soft shrink-age was superior to garrote shrinkage,which,in turn,was superior to hard shrinkage.An important exception oc-curred with the universal rule,where both the hard and garrote functions gave better estimates than the soft func-tion,regardless of the noise level.In the case of the top rule,subband-dependent semisoft shrinkage was always in-ferior to the corresponding soft shrinkage results,but the global semisoft implementation led to values comparable to those obtained with the global soft thresholding for??10 and??20.
We conclude that the choice of the shrinkage function strongly in?uences the results,and that the soft shrinkage function is preferred to either the garrote,hard,or semisoft functions.We note that,for statistical reasons,the authors in Ref.6consider only soft shrinkage.
3.2.2In?uence of shrinkage rule
The range of values in Table1indicates that the shrinkage rule strongly affects the outcome of the denoising opera-tion.In most cases,the pyramidal implementations of the rules resulted in better estimates than the global implemen-tations,regardless of the noise level.For the minFDR method,the two implementations led to very similar re-sults.For the hypTest method,the results depended on the noise level:the pyramidal version was superior for??10,but it was inferior for??20and??30.
Despite the global implementation proposed in Ref.2, we found that subband-dependent universal thresholding outperformed its global version,regardless of the shrinkage function and the noise level.
In all cases,we found that SureShrink was the best method.BayesShrink was the second best in all cases but one(??10),where the level-dependent top method was slightly better.Since we did not observe this consistently across different images and noise levels,we exclude the top rule from the list of best denoisers.However,we believe that more data-adaptive tuning is needed to choose the op-timal parameter for the top method than what we proposed in Sec.3.1.Note that in most examples reported in Ref.6, BayesShrink outperforms SureShrink.
3.2.3In?uence of noise
Our main conclusion that SureShrink and BayesShrink were the best denoisers overall is not sensitive to the amount of noise in the images.We do,however,stress that it is important to use a robust estimator of the noise,such as the MAD described in Sec.2.3.
3.2.4In?uence of wavelets
In our experiments with denoising,we found that the choice of wavelet,the number of multiresolution levels, and the boundary treatment rule had little effect on the results.This observation agrees with Ref.6.The results in Table1were obtained using the symmlet12wavelet with 12coef?cients30with K?3multiresolution levels and pe-riodic boundary treatment.We performed the same analy-ses using different wavelets,different numbers of levels,and different boundary extensions.32The ordering of the
methods,as measured by their MSE values,remained the
same for the alternatives we tried.
In our study,the biorthogonal wavelets fared worse,as
measured by the MSE,than the orthogonal symmlets.Be-
cause of their symmetry,the biorthogonal wavelets are
claimed to lead to fewer visual artifacts in reconstructed
images.10In our experiments,however,images denoised
with the nearly symmetric orthogonal symmlets are visu-
ally comparable to those obtained with biorthogonal wave-
lets.
3.2.5VisuShrink compared to SureShrink
The authors in Ref.2de?ne the term VisuShrink to refer to
global soft shrinkage with the universal threshold for1-D
signals,because it leads to visually pleasing results.How-
ever,for2-D images,just as the authors in Ref.10,we
found that SureShrink yielded much better results than the
VisuShrink procedure,both in terms of MSE and visual
quality.In fact,we found that even the global hard thresh-
olding with the universal threshold outperformed VisuSh-
rink.Though far from optimal,this global hard threshold-
ing with the universal threshold is sometimes used as a
benchmark in measuring denoising performance.Figure
3?d?displays the result of this method on‘‘Lena.’’In com-
parison,the SureShrink in Fig.3?c?results in much supe-
rior denoising.Figure4shows the corresponding details in a60?60area around the eye.SureShrink in Fig.4?c?is clearly superior,as it preserves the iris and other details
better than VisuShrink in Fig.4?d?.
In conclusion,we found that in our experiments,Sure-
Shrink and BayesShrink were the best denoisers among the
ones we studied.They yielded similar results and consis-
tently outperformed the other methods in all but one case ?the‘‘Lena’’image with??10,where the level-dependent top method with soft shrinkage resulted in a slightly
smaller MSE than BayesShrink?.In most cases,SureShrink
had slightly smaller MSE values than BayesShrink,but the
differences were small enough to be just random?uctua-
tions,and are in agreement with Ref.6.However,some
users might prefer the BayesShrink method because of its
simplicity.
For methods requiring input parameters,we could have
?ne-tuned the parameters for a given image,making the
methods more competitive.However,this requirement for
adjusting is a drawback of these methods.The two top con-
tenders,SureShrink and BayesShrink,achieved nearly op-
timal performance without relying on any parameters.
4Comparison with Spatial Filters
While wavelet-based denoising techniques are certainly a
powerful tool for image restoration,our study would be
incomplete without a comparison with the more traditional
approaches based on spatial?lters.7,34In this section,we
compare the effectiveness of denoising using several linear
and nonlinear?lters applied either by themselves or in
combination with other spatial?lters.Our choice of?lters
is listed next,with the?lter size indicated in parenthesis:
1.mean?lters(3?3,5?5).
2.Gaussian?lters(3?3,5?5).
Denoising through wavelet shrinkage...
Journal of Electronic Imaging/January2003/Vol.12(1)/157
3.Scaled unsharp masking ?lters (3?3,5?5).Given the real number ?,these ?lters calculate (1.0??)original –image-(?)mean –?ltered –image.In our experiments,???0.8gave relatively good re-sults.
4.Alpha-trimmed mean ?lters (3?3,5?5)with a trim size of either 1or 2.The trim size is the number of smallest and largest pixels that are excluded in the calculation of the mean.
5.Median ?lters (3?3,5?5).
6.Midpoint ?lters (3?3,5?5).The value calculated is the average of the minimum and maximum within the ?lter mask.
7.Minimum MSE ?lters (3?3,5?5).
For ?lters requiring an estimate of the noise variance,we used the following algorithm.First,we subtracted a (3?3)mean-?ltered image from the original.Next,we calculated the standard deviation ?SD ?of the resulting im-age,and dropped all the pixels whose absolute values were larger than the SD.Finally,we used the standard deviation of the remaining pixels as the estimate of the SD ?of the noise in the image.For the ‘‘Lena’’image with ??10,a typical estimate obtained with this method is ???10.95.The spatial ?lter-based ?ndings for the ‘‘Lena’’image are given in Table 2.The bold entries indicate the best results for the different noise levels.We used periodic boundary treatment to handle values near the edges of the image.The authors in Ref.6show empirically that the results of the best possible linear ?ltering,using the Wiener ?lter,are inferior to the results obtained with https://www.sodocs.net/doc/e39213958.html,paring the MSE values in Table 2to the corresponding values in Table 1,however,indicates that combinations of spatial ?lters can be very competitive with wavelet-based
denoising techniques.For ??20and ??30,the best spatial-?ltered images,using the 5?5minimum MSE ?lter followed by a 3?3mean ?lter,have smaller errors than the best wavelet-denoised images.
Examples of the denoised images are given in Figs.3?e
?
Fig.4Denoising results for the ‘‘Lena’’image with 60?60detail:(a)original image,(b)noisy image,(c)SureShrink,(d)global universal rule with hard thresholding,(e)minimum MSE (5?5)followed by Gaussian (3?3)?lter,(f)minimum MSE (5?5)followed by mean (3?3)?lter.
Table 2Filter-based MSE results for the ‘‘Lena’’image with periodic boundary treatment.
Image
??10
??20
??30
Noisy image 99.53399.50894.66Mean (3)42.6776.34130.46Mean (5)82.0793.91113.59Gaussian (3)32.9595.25196.92Gaussian (5)
45.5867.09101.58Scaled unsharp masking (3)34.8479.13150.75Scaled unsharp masking (5)57.7981.32119.63Alpha trimmed mean (3,1)39.1276.11134.52Alpha trimmed mean (5,2)74.2088.48110.41Median (3)40.1694.50178.17Median (5)59.3184.41120.39Midpoint (3)
78.76131.29222.31Midpoint (5)178.00196.15249.49Min-MSE (3)70.67192.53389.93Min-MSE (5)
39.3591.97163.36S-Unsharp (3),Mean (3)50.5069.0098.65Mean (3),Mean (3)54.0770.6797.35Min-MSE (5),Mean (3)44.9564.8089.44Min-MSE (5),Gaussian (3)31.7856.8088.52S-Unsharp (3),Gaussian (3)41.5666.99107.81Gaussian (3),Gaussian (3)
37.09
68.64
119.50
Fodor and Kamath
158/Journal of Electronic Imaging /January 2003/Vol.12(1)
and 3?f ?,with corresponding details in Figs.4?e ?and 4?f ?.Based on the MSE values,the ?ltered images in Figs.3?e ?and 4?e ?are superior to the SureShrink-denoised images in Figs.3?c ?and 4?c ?.A visual comparison of the full images in Fig.3indicates that overall,the two images are compa-rable.However,the zoomed-in panels in Fig.4show that,while the iris in the eye is preserved in the wavelet-denoised image,it disappears in the ?ltered images.In gen-eral,spatial ?lters result in grainier images than the ones obtained from wavelet techniques.Unless special care is taken near the edges,they also tend to smooth the edges in the image.On the other hand,wavelet-based approaches,if not selected carefully,can create noticeable artifacts that substantially degrade the image.
To supplement our results obtained using test images,Fig.5illustrates some of the techniques on a real medical angiogram.35Figure 5?a ?shows the 72-?72-pixel original,with gray-scale values in ?0,132?.Since the noiseless ‘‘truth’’is unknown in this case,we can only evaluate vi-sually the denoisers.Figure 5?b ?displays the result of ap-plying twice the 3?3Gaussian ?lter with coef?cients 132
?14
1
4
1241
41
?
.?27?
As with the test images,two applications of the spatial ?lter suppressed more noise than just one application,at the ex-pense of introducing slightly more blur.The four wavelet-denoised images in Figs.5?c ?through 5?f ?were obtained with the symmlet8wavelet on three multiresolution levels.To estimate the noise standard deviation ?,required by some of the thresholding methods,we used the scaled MAD of the ?nest level diagonal detail coef?cients,as mentioned in Sec.3.1,and explained in Refs.1and 36.The
value of the estimate is ?
??3.94.The results of the best two wavelet-denoisers based on the test images,SureShrink and BayesShrink,are displayed in Figs.5?c ?and 5?d ?,respec-tively.Neither introduces artifacts,and both preserve the main features of the original image.However,unlike in the case of the test images,they do not satisfactorily remove the noise from this angiogram.Just as with the test images,hard thresholding with the universal rule creates many ar-tifacts,as shown in Fig.5?e ?.We obtained the best wavelet-based denoising by applying soft thresholding with the top rule,keeping 30%of the largest coef?cients.Overall,the result of this simple method displayed in Fig.5?f ?is supe-rior to the rest of the images in Fig.5.
Spatial ?lters are very easy to implement and computa-tionally inexpensive as they involve just a simple convolu-tion.In contrast,each of the wavelet-based methods in-cludes a forward and inverse discrete wavelet transform which requires O (N )operations,where N is the number of pixels in the image.There is also an additional cost of calculating the shrinkage rule and applying the shrinkage function.The latter requires O (N )comparisons and O (N )operations.The computation for the shrinkage rule varies from negligible in the case of the universal rule to several N s log(N s )operations for the SURE threshold.Most of this cost is due to the sorting of the N s wavelet coef?cients on subband s .Given the speed and memory of current com-puter systems,none of the methods is computationally ex-pensive.For example,on a Dell Precision 530workstation ?32-GB disk,512-MB memory,dual 1.5-GHz Intel Xeon processors ?running the RedHat Linux operating system,it takes only a few seconds for our C ??software to perform SureShrink denoising on a 512?512single-precision ?oat-ing point image.
5Summary
We evaluated several denoising methods on test images corrupted with additive Gaussian white noise.We consid-ered an extensive set of techniques based on statistical thresholding of wavelet coef?cients as well as more tradi-tional approaches using spatial ?lters.
Based on our experiments,we conclude that SureShrink and BayesShrink are the best wavelet-based denoising methods for the types of images we considered,among the methods we considered.None of the other wavelet-based procedures that we examined achieved lower error rates,as measured by the MSE,than these two techniques.When we consider simplicity of implementation along with the de-noising performance,we found BayesShrink to be the best procedure.
For completeness,we also compared the wavelet-based denoisers with various spatial ?lter-based methods.On a case-by-case basis,it is often possible to ?nd a
denoiser
Fig.5Denoising results for a medical image:(a)original image,(b)Gaussian (3?3)?lter applied twice,(c)SureShrink,(d)BayesShrink,(e)global universal rule with hard thresholding,and (f)global top rule with soft thresholding.
Denoising through wavelet shrinkage ...
Journal of Electronic Imaging /January 2003/Vol.12(1)/159
based on combinations of spatial?lters that is superior,in terms of MSE,to the best wavelet-based denoiser.In most, but not all,of those cases,the optimal method is given by applying the5?5Min-MSE?lter followed by the3?3 Gaussian?lter.In terms of visual quality,however,the SureShrink wavelet-based denoiser was the only method that preserved a feature of interest,namely,the iris in the eye of‘‘Lena.’’
Recently,several alternative denoising techniques have been introduced in the literature.We plan to complement our study by exploring some of those newer techniques as well.
Acknowledgments
This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under Contract https://www.sodocs.net/doc/e39213958.html,wrence Livermore National Labo-ratory release number:UCRL-JC-144258.
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Imola K.Fodor received her PhD degree in statistics from the Uni-versity of California,Berkeley,in1999.She is a computational math-ematician with the Center for Applied Scienti?c Computing, Lawrence Livermore National Laboratory,California.Her current re-search interests include signal processing and statistical issues in data mining.
Chandrika Kamath received her PhD degree in computer science from the University of Illinois,Urbana-Champaign,in1986.She is a computer scientist and project leader with the Center for Applied Scienti?c Computing,Lawrence Livermore National Laboratory, California.Her research interests include image processing,pattern recognition,and practical applications of data mining.She is a mem-ber of ACM,IEEE,SIAM,and SPIE.
Fodor and Kamath 160/Journal of Electronic Imaging/January2003/Vol.12(1)
介词by用法归纳-九年级
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. . 教学过程 一、课堂导入 本堂知识是初中最常见的介词by的一个整理与总结，让学生对这个词的用法有一个系统的认识。页脚.
. . 二、复习预习 复习上一单元的知识点之后，以达到复习的效果。然后给学生一些相关的单选或其他类型题目，再老师没有讲解的情况下，让学生独立思考，给出答案与解释，促进学生发现问题，同时老师也能发现学生的盲点，并能有针对性地进行后面的讲课。 页脚.
. . 三、知识讲解 知识点1： by + v.-ing结构是一个重点，该结构意思是“通过……，以……的方式”，后面常接v.-ing形式，表示“通过某种方式得到某种结果”，即表示行为的方式或手段。 I practice speaking English by joining an English-language club. 我通过加入一个英语语言俱乐部来练习讲英语。 Mr Li makes a living by driving taxis.先生靠开出租车为生。 页脚.
. . 页脚. 介词by + v.-ing 结构常用来回答How do you...?或How can I...?之类的问题。 —How do you learn English? 你怎样学习英语呢？ —I learn English by reading aloud. 我通过大声朗读来学英语。 —How can I turn on the computer? 我怎样才能打开电脑呢？ —By pressing this button. 按这个按钮。 知识点2：by 是个常用介词，其他用法还有： 1【考查点】表示位置，意思是“在……旁边”，“靠近……”，有时可与beside互换。 The girls are playing by (beside) the lake. 女孩们正在湖边玩。 此时要注意它与介词near有所不同，即by 表示的距离更“近”。比较： He lives by the sea. 他住在海滨。 He lives near the sea. 他住在离海不远处。
浅谈混凝土表面干缩裂缝成因及防治办法
浅谈混凝土表面干缩裂缝成因及防治办法 发表时间：2018-10-17T16:37:41.003Z 来源：《防护工程》2018年第12期作者：邵明安 [导读] 基础不均匀沉降；拆模过早；结构性破坏；临时放置位置不当（如箱梁、空心梁板的支座不在永久支座处）；施加预应力时混凝土强度不足。限于篇幅等原因，本文仅从温度和湿度变化引起的混凝土干缩裂缝进行分析探讨。 邵明安 临沂市建设工程监理公司山东省 276000 混凝土表面裂缝几乎无处不在，或呈线形分布或成网状分布，或者有规律分布，或者无规则分布。从混凝土浇筑成型至构件的使用期，混凝土的裂缝几乎伴随其终生。就其产生的原因，无外乎以下几点：温度和湿度的变化；混凝土的脆性和不均匀性；结构不合理；碱骨料反应；模板变形；基础不均匀沉降；拆模过早；结构性破坏；临时放置位置不当（如箱梁、空心梁板的支座不在永久支座处）；施加预应力时混凝土强度不足。 限于篇幅等原因，本文仅从温度和湿度变化引起的混凝土干缩裂缝进行分析探讨。 1干缩裂缝产生的原因 混凝土初期硬化期间水泥放出大量的水化热，内部温度不断上升，在混凝土表面形成拉应力，后期降温过程中，由于受到其他混凝土构件的约束，又会在混凝土内部出现拉应力。同时，气温（或者混凝土表面温度）也会在混凝土表面引起很大的拉应力。当这些拉应力超出混凝土的抗裂能力时，便会出现裂缝。 绝大多数混凝土内部湿度变化很小，同时变化也很慢，但表面湿度变化较大而剧烈。这主要是因为养护不到位、时干时湿，表面干缩变形受到内部混凝土的约束，使表面混凝土受到拉力，导致表面出现裂缝。 众所周知，混凝土是一种脆性的不均匀性的材料，抗拉强度只有抗压强度的1/10左右。加之，原材料的不均匀性、集料级配的不合理性、水灰比的不稳定性。运输和浇筑过程的离析现象，振捣过程中出现漏振或者过振的现象，形成一个一个层面，在同一个混凝土构件中，其抗拉强度也不均匀，存在很多抗拉能力很低、易于出现裂缝的薄弱部位。在钢筋混凝土中，拉应力主要由钢筋承担，混凝土只承受压应力。如果在其边缘部位出现拉应力，那么只能依靠混凝土自身来承担。如果产生的拉应力大于混凝土的抗拉强度。便形成了裂缝。 2通过温度的控制减少裂缝产生的措施 根据前面的分析，混凝土表面的裂缝是因温度变化形成的拉应力引起的。那么就从控制温度和改善约束条件两方面着手解决。而温度的控制我们又从减少混凝土内部的水化温度和外环境的气温剧变两方面考虑。具体办法有：（1）改善骨料级配。严禁使用单粒级配，采用2种甚至3种粒径段的集料（碎石），进行科学合理的掺配。骨料级配合理可减少水泥用量，而减少水泥用量便可以减少水泥的水化热。同时，改善混凝土的不均匀性，提高混凝土的抗拉强度。 （2）严格控制混凝土的坍落度，通过减少用水量和水泥用量，来控制混凝土的温度应力。 （3）避开高温浇筑混凝土，如果气温高于30℃尽量不要浇筑混凝土，条件实在不允许，可采用对模板降温，给碎石降温，减少混凝土浇筑层等办法。 （4）确定合理的拆摸时间，气温骤降时进行表面保温，以免混凝土表面发生急剧的温度梯度。 （5）施工中长期暴露的混凝土，在寒冷季节采取保温措施。 （6）冬期施工时，如果采用蒸汽养护，需要注意3点，慢升温，慢降温，避高温，以免混凝土表面形成急剧的温度梯度。 （7）拆模后，混凝土一定要做好保温养护，严防常期暴露在高温、干燥、风多的自然环境中，也要杜绝干湿循环，应当覆盖洒水养护，使混凝土表面处于长期湿润状态。既降低混凝土环境温度，又防止表面干缩出现裂缝。特别是混凝土早期的前7天，水化热大，混凝土强度及弹性模量急剧变化。内部产生残余应力，与温度应力进行迭加，而混凝土本身抗拉抗裂性就差，这个时期则更低。因此养护不好更容易出现裂缝。 （8）合理进行分缝分块。 （9）对于地下工程可采用早回填早覆盖。 （10）在混凝土终凝前用木抹子压抹一次，混凝土表面形成微膜并把细小裂缝处理掉。 （11）严格控制钢筋的保护层，若钢筋保护层不足，因收缩沿钢筋位置出现裂缝。 （12）混凝土拆模后应即时覆盖，防止因风吹，减少混凝土表面的水分。 3减水剂的使用对减少混凝土表面裂缝的重要作用 （1）由于混凝土中存在大量的毛细孔道，水分蒸发后毛细管中产生毛细管张力，导致混凝土出现干缩变形。因此，掺合减水剂可以减少水分，从而减少毛细管张力，起到减少于缩变形的可能性。 （2）水灰比是影响混凝土收缩的重要因素，使用减水剂可使混凝土用水量减少25％左右。 （3）水泥用量也是混凝土收缩率的重要影响因素，掺加减水剂的混凝土在保持强度不变的情况下，可减少15％左右的水泥用量。 （4）掺加减水剂还可以改善水泥浆的稠度，减少混凝土的泌水，从而减少混凝土的沉缩变形。 （5）由于减少了用水量，因此减少了水分蒸发后形成的空穴，从而提高了水泥浆与骨料的黏结力，进而提高混凝土的抗裂性能，减少裂缝。 （6）掺加减水剂可使混凝土的密实性提高，从而有效地提高混凝土的抗碳化性，减少碳化收缩。 （7）减水剂一般对混凝土有缓凝作用。但时间恰当，因此在有效防止水泥迅速水化放热基础上，避免因水泥长期不凝造成塑性收缩增加。 （8）减水剂可以改善混凝土的和易性，表面容易抹平，形成微膜，减少水分蒸发，从而减少干缩。 4结束语
Through 的用法
Through 的用法 （一）作介词 (1) 从…中通过;贯穿,穿过(强调丛物体内部或一定范围内),透过 We started to push our way through crowds of children、 The River Thames flows through London、On our way we had to pass through Hudson Street、 The sunlight was coming in through the window、The sound echoed through the hall、(2)通过,凭借(方法手段),经由 He became rich through hard work and ability、 We learn to speak through speaking、He got the job through his uncle、 (3)由于,因为…的关系 He failed through lack of experience、 (4)自始至终;从头到尾/底 The children are too young to sit through a long concert、 We worked through the night、 (5)经受;经历 That was a small matter after the Cultural Revolution they had been through、辨析:through ,across ,over (复习) The Great Wall winds its way from west to east, _______ deserts, _______ mountains, ______ valleys, till at last it reaches the sea、 Go _______ the bridge _______ the river, and you will find the shop、 I have made friends right ________ the world、 The crowd of people walked past the City Hall to the Center Square、 Through & by 表示“通过”时,through 后常加名词表示手段媒介,而by 后常加工具具 体名词以及-ing 形式。 He got that job through his uncle、 You can succeed by working hard、I sent the letter by airmail、 (二) 作副词 (1) 通过,过去(可与许多动词连用) The flood is too deep to drive through、 (2) 彻底地;接通电话 Don’t tell me how it ends---I haven’t read it through、 You’re through to London, sir! (三) 常见搭配 Get through ①通过;度过 He got through his examinations、 ②做完;吃完;饮完 We managed to get through the work in four hours、
by与through的区别
By 与through 的区别 1．by （1）表示方法，手段。即“用...，通过...以…方式 ”相当于by means of 如： All work had to be done by hand 所有的工作都是手工进行的。 He makes a living by teaching 他以教书为生。 It happened through no fault of mine.这件事的发生, 并非由于我的任何过错。 He saluted her by raising his hat.他举起帽子向她致意。 She earned money by writing.她靠写作挣钱。 根据；按照to play by the rules按规则比赛 相差His horse won by a nose.他的马以一鼻之差取胜。 （2）表示传达、传递的方式或煤介。如： How did you send the letter, by airmail or by ordinary mail？ 你是怎么发送的这信，是通过航天邮件还是普通邮件？ （3）表示用交通工具、通讯工具后接名词单数，不加冠词。如： He came by train, but his wife came by bus. 他是乘火车来的，可是他老婆是坐公共汽车来的。 注意下面两句的区别： Did you come by train =Did you come in his car / on my bike？ “by +抽象名词”构成的词组有： by accident / by chance / by diligence / by effort / by force / by heart / by luck / by mistake / by hard work. （4）指数量增加或减少到的程度，相差。 We lost the match by one goal 我们仅以一球之差输了比赛。 （5）根据，按照 pay sb by the hour /day/week Sell sth by the pound /meter/ dozen sell sth by weight/length As a rule，domestic servants doing odd jobs are paid by the hour 通常，家政服务是按照小时计酬的。 They marched by night.他们夜里进军。 2. through （1）表示“以；通过；经由”。如：
大体积混凝土干缩裂缝的原因与预防
大体积混凝土干缩裂缝的原因与预防 现代工程整浇混凝土都具有不同程度的大体积混凝土的性质，尤其C50以上混凝土水泥用量大，水灰比较小，对干燥收缩有利（过低水灰比对早期塑性收缩和自生收缩不利），但由于水泥浆量较多以及高效减水剂的作用，总收缩可比中低强度混凝土大，并且拉压强度比降低，徐变小，应力松弛低，脆性高容易引起开裂。本文对高强混凝土施工过程中容易产生收缩裂缝的原因进行分析： 一、含水量，含水量越高，表现为水泥浆量或含胶浆量越大，坍落度大，收缩越大。收缩越大的混凝土拆模过早，表面早期大量失水易产生裂缝。施工过程中应严格控制坍落度，避免雨中浇筑混凝土，严禁现场加水。 二、原材料质量，粗细骨料中含泥量越大收缩越大，骨料粒径越细，砂率越高，收缩越大，水泥活性越高，颗粒越细比表面积越大，收缩越大，超细掺合料具有相同性质。混凝土近代发展高效化学外加剂和矿物掺合料作为第五、第六组分掺入，有利于提高混凝土的耐久性，但是应当注意原材料的用量和质量。大掺量高性能混凝土的早期塑性收缩和自生收缩较大，易引起开裂。必须严格控制原材料质量，不宜采用吸水率大的骨料及掺合料（骨料可以预先水洗）。重视外加剂掺量（要检测称量装置的可靠性）的准确性和敏感性，掺量过多过少会造成质量事故。
三、早期养护，养护时间过短，收缩大易产生裂缝。应适当延长早期养护时间，拆模后宜覆盖塑料薄膜，加强潮湿养护对控制早期塑性裂缝很有益处。 四、注意振捣，特别是在交接处，超振会造成混凝土离析和大量泌水，表面失水过快，早期收缩越大，表面容易产生裂缝。 五、环境，施工过程中如果风速较大，收缩就越大，封闭或开敞环境中的裂缝程度取决于环境温湿度变化，水化温升，里表温差及降温速率相差大易产生裂缝。应当控制较低的入模温度，在天气好的情况下施工，尽量避免中午高温时段进行浇筑。 混凝土工程是桥梁的重要组成部分，施工过程中现场技术人员、拌合站、试验室应相互配合，及时沟通，保证混凝土施工过程中的连续稳定，才能造就完美工程。
介词的用法2
一、介词的分类介词可分为三类： 1.简单介词：由一个单词构成的介词。如：about, after, but, for, from, below等。 2.复合介词：由两个或两个以上单词合成的介词，如：into, throughout，onto，within，without, nearby 等。 3.短语介词：一个或两个简单介词和一个或几个其他词类组合成一个短语，相当于一个介词，叫做短语介词，这类介词的末尾总是一个简单介词。如：according to, because of, out of, in front of, instead of, along with等。 二、介词短语的用法：介词短语作为一个成分在句中可用作定语、状语、表语、宾语补足语等。 1.作定语：介词短语作定语时，一般放在被修饰词的后面，作后置定语。 The book on the desk is very interesting. 书桌上的那本书很有趣。 China is a great country with a long history. 中国是一个具有悠久历史的国家。 2.作状语：介词短语作状语时，一般放在动词后面或句末、句首。用来表示时间、地点、目的、方式和原因等。 The basketball match will start at nine. 篮球比赛将在9点开始。（表示时间）He likes to swim in the river. 他喜欢去河里游泳。（表示地点）I went there to get my book back. 我去那里取回我的书。（表示目的）I came here by bike. 我骑自行车来到这里。（表示方式）She was trembling with fear. 她吓得直发抖。（表示原因）3.作表语：介词短语作表语时，一般放在be动词和连系动词之后。 I'm on duty today. 今天我值日。My English teacher is from Australia. 我的英语老师来自澳大利亚。(4)作宾语补足语：介词短语作宾语补足语时，一般放在宾语之后。 Help yourself to some fish. 请吃鱼。I found everything ill good condition. 我发现一切状况良好。 We all think of him as an honest man. 我们都认为他是一个诚实的人。 三、常用介词的意义及用法 （一）表示时间的介词：英语中表示时间的介词很多，主要有以下这些：at, on，in, after，for，since, by，till，until等。 1. at的用法时间介词at表示时刻或时间的某一点。如：at 4: 30 (noon, dawn, midnight... )在4: 30（中午、黎明、午夜） 2.on的用法：时间介词on表示日期及某天的上午、下午、晚上等。如：on Sunday (Oct. 1... )在星期日（10月1日……）on Sunday afternoon星期日下午，另也可说：in the afternoon on Sunday 特别提示：关于“在周末”的几种表示法： at (on) the weekend （在周末——特指）at (on) weekends （在周末——泛指）over the weekend （在整个周末）during the weekend （在周末期间）。在圣诞节，应说"at Christmas", 而不说"on Christmas"。 3.in的用法 (1)时间介词in表示“时段，时期”，在多数情况下可以和during互换，前者强调对比，后者强调持续。如： in (during) 1987在1987年in (during) the 21st century在21世纪 但是如果表示“在某项活动的期间”，则只能用during。如：during the trip...在旅行期间…… (2)时间介词in表示以说话时间为基点的“若干时间以后”，常用于谓语是将来时的时间状语。如要表示“若干时间内”，则常用within。试比较：The meeting will end in 30 minutes. 会议30分钟以后结束。Can you finish it within 30 minutes? 你能在30分钟之内完成这件事吗？ 但是在过去时态中，in和within的意思一样，并都可用于表示“在若干时间以内”，这时不要误用during。如： The job was done during a week. (x) The job was done in a week. (√) 4.after的用法 时间介词after表示“在（某具体时间）以后”，注意不要和in混淆。如：after supper (5 o'clock, the war,
浅谈混凝土表面干缩裂缝防治措施
浅谈混凝土表面干缩裂缝防治措施 发表时间：2012-08-27T10:18:40.887Z 来源：《赤子》2012年第6期作者：谢贰军 [导读] 当这些拉应力超出混凝土的抗裂能力时，便会出现裂缝。 谢贰军（广西富林劳务有限公司，广西南宁 530022） 摘要：混凝土是当前建筑工程施工中主要的施工原材料之一，随着当前社会的不断发展，人们对混凝土认识日益增加，在混凝土施工中对其各种施工缺陷的管理和控制方式手段不断的增加。在混凝土施工中，表面干缩裂缝的形成是其主要的质量隐患和缺陷。结合本人的多年实践，针对混凝土表面出现的干缩裂缝，通过在施工中的各种原理和缺陷因素进行综合分析，提出其在施工中的主要处理手段和处理方法。 关键词：混凝土；干缩裂缝；防治办法 混凝土是当前建筑工程施工中主要的施工形式，由于其物美价廉，取材方便，施工技术简单和耐久性能高成为当前建筑工程应用的主要方式。混凝土表面裂缝几乎无处不在，或呈线形分布或成网状分布，其裂缝出现的过程中是一种无规律的分布状况和分布方法，其在施工的过程中如何解决和提高其裂缝的出现措施和出现方法是当前建筑工程在施工中探讨的重点。从混凝土浇筑成型至构件的使用期，混凝土的裂缝几乎伴随其终生。其混凝土裂缝的产生原因主要是有以下几点：温度和湿度的变化；混凝土的脆性和不均匀性；在施工中构造结构的不合理，以及在混凝土配合中各种原材料应用的不够准确和完善，在施工的时候由于施工环节控制不严谨，模板变形；基础不均匀沉降；拆模过早；结构性破坏，临时放置的时候选用放置的位置不恰当，造成混凝土在施工中出现了诸多的裂缝因素和产生方式。 1 干缩裂缝产生的原因 混凝土初期硬化期间水泥放出大量的水化热，使得在混凝土凝结的过程中内部温度不断的提高和上升，造成混凝土在干缩的时候其表面温度不断的提高，其在发展中出现了诸多的裂缝和制约影响因素是当前混凝土表面应拉力出现了巨大的变化。后期降温过程中，由于受到其他混凝土构件的约束，又会在混凝土内部出现拉应力。同时，气温（或者混凝土表面温度）也会在混凝土表面引起很大的拉应力。当这些拉应力超出混凝土的抗裂能力时，便会出现裂缝。 绝大多数混凝土内部湿度变化很小，同时变化也很慢，但表面湿度变化较大而剧烈。这主要是因为养护不到位、时干时湿，表面干缩变形受到内部混凝土的约束，使表面混凝土受到拉力，导致表面出现裂缝。 众所周知，混凝土是一种脆性的不均匀性的材料，抗拉强度只有抗压强度的1/10左右。加之，原材料的不均匀性、集料级配的不合理性、水灰比的不稳定性。运输和浇筑过程的离析现象，振捣过程中出现漏振或者过振的现象，形成一个一个层面，在同一个混凝土构件中，其抗拉强度也不均匀，存在很多抗拉能力很低、易于出现裂缝的薄弱部位。在钢筋混凝土中，拉应力主要由钢筋承担，混凝土只承受压应力。如果在其边缘部位出现拉应力，那么只能依靠混凝土自身来承担。如果产生的拉应力大于混凝土的抗拉强度。便形成了裂缝。 2 通过温度的控制减少裂缝产生的措施 凝土是一种由砂石骨料、水泥、水及其他外加材料混合而形成的非均质脆性材料。由于混凝土施工的过程中各种施工工艺和施工方式日益完善，在施工的过程中是通过相关的技术措施技术管理手段进行分析与应用。根据前面的分析，混凝土表面的裂缝是因温度变化形成的拉应力引起的。那么就从控制温度和改善约束条件两方面着手解决。而温度的控制我们又从减少混凝土内部的水化温度和外环境的气温剧变两方面考虑。具体办法有： （1）改善骨料级配。严禁使用单粒级配，采用2种甚至3种粒径段的集料（碎石），进行科学合理的掺配。骨料级配合理可减少水泥用量，而减少水泥用量便可以减少水泥的水化热。同时，改善混凝土的不均匀性，提高混凝土的抗拉强度。（2）严格控制混凝土的坍落度，通过减少用水量和水泥用量，来控制混凝土的温度应力。 （3）避开高温浇筑混凝土，如果气温高于30℃尽量不要浇筑混凝土，条件实在不允许，可采用对模板降温，给碎石降温，减少混凝土浇筑层等办法。 （4）确定合理的拆摸时间，气温骤降时进行表面保温，以免混凝土表面发生急剧的温度梯度。（5）施工中长期暴露的混凝土，在寒冷季节采取保温措施。 （6）冬期施工时，如果采用蒸汽养护，需要注意3点，慢升温，慢降温，避高温，以免混凝土表面形成急剧的温度梯度。（7）拆模后，混凝土一定要做好保温养护，严防常期暴露在高温、干燥、风多的自然环境中，也要杜绝干湿循环，应当覆盖洒水养护，使混凝土表面处于长期湿润状态。既降低混凝土环境温度，又防止表面干缩出现裂缝。特别是混凝土早期的前7天，水化热大，混凝土强度及弹性模量急剧变化。内部产生残余应力，与温度应力进行迭加，而混凝土本身抗拉抗裂性就差，这个时期则更低。因此养护不好更容易出现裂缝。 （8）合理进行分缝分块。 （9）对于地下工程可采用早回填早覆盖。 （10）在混凝土终凝前用木抹子压抹一次，混凝土表面形成微膜并把细小裂缝处理掉。 （11）严格控制钢筋的保护层，若钢筋保护层不足，因收缩沿钢筋位置出现裂缝。 （12）混凝土拆模后应即时覆盖，防止因风吹，减少混凝土表面的水分。 3 减水剂的使用对减少混凝土表面裂缝的重要作用 （1）由于混凝土中存在大量的毛细孔道，水分蒸发后毛细管中产生毛细管张力，导致混凝土出现干缩变形。因此，掺合减水剂可以减少水分，从而减少毛细管张力，起到减少于缩变形的可能性。 （2）水灰比是影响混凝土收缩的重要因素，使用减水剂可使混凝土用水量减少25％左右。（3）水泥用量也是混凝土收缩率的重要影响因素，掺加减水剂的混凝土在保持强度不变的情况下，可减少15％左右的水泥用量。（4）掺加减水剂还可以改善水泥浆的稠度，减少混凝土的泌水，从而减少混凝土的沉缩变形。（5）由于减少了用水量，因此减少了水分蒸发后形成的空穴，从而提高了水泥浆与骨料的黏结力，进而提高混凝土的抗裂性能，减少裂缝。 （6）掺加减水剂可使混凝土的密实性提高，从而有效地提高混凝土的抗碳化性，减少碳化收缩。
图解英语介词的基本用法
AT The ball is at the edge of the table. WITH The black brick is with the ball. FROM The ball is going from the hand. AGAINST The black brick is against the white b rick. TO The ball is going to the hand. ACROSS The black rod is across the white rod. AFTER3is after2. AMONG The ball is among the bricks. BEFORE1is before2. ABOUT The bricks are about the ball. THROUGH The rod is through the board. DOWN The ball is down. BETWEEN The ball is between the bricks. UP The ball is up. UNDER The ball is under the arch. ON The ball is on the table. OVER The arch is over the ball. OFF The ball is off the table. BY The ball is by the arch. IN The ball is in the bucket. OUT The ball is out of the basket.
介词用法归纳
介词（preposition） 又称前置词，是一种虚词。介词不能单独做句子成分。介词后须接宾语，介词与其宾语构成介词短语。 一、介词从其构成来看可以分为： 1、简单介词（Simple prepositions）如：at ,by, for, in, from, since, through等； 2、复合介词（Compound prepositions）如：onto, out of, without, towards等； 3、短语介词（phrasal prepositions）如；because of, instead of, on account of, in spite of, in front of等； 4、二重介词（double prepositions）如：from behind, from under, till after等； 5、分词介词（participial prepositions），又可称动词介词（verbal prepositions）如：during, concerning, excepting, considering, past等。 二、常见介词的基本用法 1、 about 关于 Do you know something about Tom？ What about this coat？（……怎么样） 2、 after 在……之后 I’m going to see you after supper. Tom looked after his sick mother yesterday.（照看） 3、 across 横过 Can you swim across the river. 4、 against 反对 Are you for or against me? Nothing could make me turn against my country.（背叛） 5、 along 沿着 We walked along the river bank. 6、 before 在……之前 I hope to get there before seven o’clock. It looks as though it will snow before long.（不久） 7、behind 在……后面 The sun is hidden behind the clouds. 8、by 到……时 We had learned ten English songs by the end of last term. 9、during 在……期间 Where are you going during the holiday. 10、except 除了 Everyone except you answered the question correctly. 11、for 为了 The students are studying hard for the people. 12、from 从 I come from Shanghai. 13、in 在……里 on 在……上面 under在……下面 There are two balls in/on/under the desk. 14、near 在……附近 We live near the park. 15、of ……的 Do you know the name of the winner. 16、over 在……正上方 There is a bridge over the river. Tom goes over his English every day.（复习） 17、round/around 围绕 The students stand around the teacher. 18、to 朝……方向 Can you tell me the way to the cinema. 19、towards朝着 The car is traveling towards Beijing.
七个经过” pass, cross, through, by……怎么过(有何区别).doc
七个经过” pass, cross, through, by…… 怎么过（有何区别） 这7个表”经过“的词中，除pass, cross是动词外，其它都是介词（副词）。首先，我们从词性上去区别它们。 充当谓语动词时用pass, cross, 不充当谓语动词时用past, across, through, over, by从旁边“经过”“绕过” “路过”用pass （介词形式为past）, 从表面“越过”用cross（介词形式为across）img src=https://www.sodocs.net/doc/e39213958.html,/large/pgc-image/15251329904161dc24 05d4e img_width=474 img_height=266 alt=七个经过”= pass,= cross,= through,= by……怎么过（有何区别）= inline=0 style=box-sizing: border-box; -webkit-tap-highlight-color: transparent; border-style: none; max-width: 100%; display: block; margin: 10px auto; Light goes through the window 不充当谓语时，几个介词“经过”的区别 past从旁边“经过”“路过”“绕过”by从旁边“经过”“绕过”“绕过”（此时by=pst）across 从表面“经过” , 空中“越过”（比如把东西从房间的一边扔到另一边）over 1. 从上方“经过”“飞过” “跨过”；2.从表面“经过”“越过”（此时over=across）through从内部“穿过”为何以上单词用法孩子们不容易分得清，而“man和child却不可能弄错？因为前者的汉语意思相
造成混凝土干缩裂缝的原因有
造成混凝土干缩裂缝的原因有，施工单位对混凝土的养护不良，使表面水分蒸发过快，体积收缩，而楼板内部湿度变化较小。避免在混凝土施工过程中出现肝裂缝，施工单位应采取防护措施。1。混凝土水泥用量、水灰比和砂率不能过大，严格控制砂石含泥量，避免食用过量粉沙，振捣要密实，并对板面进行二次压抹，提高混凝土抗拉强度，减少干缩。2。加强混凝土早期养护，并适当延长养护时间；3。浇筑混凝土前将基层模板浇水湿透。4。混凝土浇筑后应及早进行洒水养护，楼板干缩裂缝对结构强度影响不大，但会使钢筋锈蚀，影响美观，处理意见，一般可在表面抹一层薄砂浆进行处理。 工程混凝土楼板出现裂缝的现象比较常见，现根据有关资料，对现浇混凝土楼板和砌块填充墙裂缝的原因和对策分析如下，供参考。 一、现浇混凝土楼板裂缝的类型 1．纵向裂缝：即沿建筑物纵向方向的裂缝，出现在板下皮居多，个别上下贯通。 2．横向裂缝：即在跨中1/3范围内，沿建筑物横向方向的裂缝，出现在板下皮居多，个别上下贯通。 3．角部裂缝：在房间的四角出现的斜裂缝，板上皮居多。 4．不规则裂缝：分布及走向均无规则的裂缝。 5．楼板根部的横向裂缝：距支座在30cm内产生的裂缝，位于板上皮。 6．顺着预埋电线管方向产生的裂缝。 二、楼板产生裂缝的原因 1.设计方面 1．1 设计结构时安全储备偏小,配筋不足或截面较小，使梁板成型后刚度差，整体挠度偏大，引起板四角裂缝。 1．2 设计板厚不够，又不做挠度验算，整体挠度偏大，引起板四角裂缝。 1．3 房屋较长时未设置伸缩缝，在薄弱环节产生收缩裂缝。（美国混凝土学会的资料认为混凝土有干缩和温度变形两种，干缩变形每30.48m约收缩19mm。温度变化引起的变形为,37℃的温度变化每30.48m 收缩或延长19mm 左右。国内有人认为40m 长的楼板因硬化凝固产生的纵向收缩量为8—20mm。） 1.4 基础设计处理不当，引起不均匀沉降，使上部结构产生附加应力，导致楼板裂缝。 1．5 楼板双向受力，按单向板配筋，引起裂缝。 2．商品混凝土原因 2．1 水灰比大，水泥用量大。 2．2 高效缓凝剂用量过大，在未凝固前石子下沉，产生沉缩裂缝，常发生在梁板交接处。 2．3 砂石质量不好，级配不好，含泥量大，含粉量大。 3 施工原因 3．1 养护不到位，强制性规范要求混凝土养护要苫盖并浇水，现在大多数不苫盖，浇水也不能保证经常性湿润。 3．2 施工速度过快，上荷早，特别是砖混住宅楼板，前一天浇筑完楼板，第二天即上砖、走车，造成早期混凝土受损。 3.3 冬时期间受冻。 3．4 拆模过早或模板支撑系统刚度不够。 3．5 混凝土表面浮浆过厚，表面强度不够。 3．6 施工时楼板混凝土盖筋被踩弯、踩倒，保护层过厚，承载力下降。
介词的用法总结
介词的用法 1.表示地点位置的介词 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边” in (1)表示在大地方; (2)表示“在…范围之内”。 on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line. 4)in front [frant]of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。 There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。 There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。 Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边 behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时 in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。 如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one?s life , in one?s thirties等。 on表示具体某一天及其早、中、晚。 如on May 1st, on Monday, on New Year?s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。 at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。 如at 3:20, at this time of year, at the beginning of, at the end of …, at the age of …, at Christmas，at night, at noon, at this moment等。 注意：在last, next, this, that, some, every 等词之前一律不用介词。如：We meet every day.
介词用法归纳总结
介词 介词是一种用来表示词与词、词与句之间的关系的虚词，在句中不能单独作句子成分。介词后面一般有名词代词或相当于名词的其他词类，短语或从句作它的宾语。介词和它的宾语构成介词词组，在句中作状语，表语，补语或介词宾语。介词可以分为时间介词、地点介词、方式介词、原因介词和其他介词， 1.表示地点位置的介词 1)at ,in, on, to at (1)表示在小地方; (2)表示“在……附近，旁边” in (1)表示在大地方; (2)表示“在…围之”。 on 表示毗邻，接壤，“在……上面”。 to 表示在……围外，不接壤；或“到……” eg: in the east of China(在中国的东部) on the east of China(在与中国的东部接壤的地方) to the east of China(在中国以东) 2)above, over, on 在……上 above 表示一个物体高过另一个物体,不强调是否垂直，与below相对； over一个物体在另一个物体的垂直上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示一个物体在另一个物体表面上，并且两个物体互相接触与beneath相对。 The bird is flying above my head.（这只鸟飞在我的头上） There is a bridge over the river.（河上有一座桥） He puts his watch on the desk.（他把他的手表放在桌子上） 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table.（有一只猫在桌子底下） Please write your name below the line.（请把你的名字写在线下） 4)in front [frant]of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。 There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的部.反义词是at the back of…（在……围的后部）。 There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。 Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind , between beside 表示在……旁边 behind 表示在……后面 between表示在两者之间 6) on the tree, in the tree on the tree 长在树上 in the tree 外来落在树上
介词by用法归纳 九年级
教学过程 一、课堂导入 本堂知识是初中最常见的介词by的一个整理与总结，让学生对这个词的用法有一个系统的认识。
二、复习预习 复习上一单元的知识点之后，以达到复习的效果。然后给学生一些相关的单选或其他类型题目，再老师没有讲解的情况下，让学生独立思考，给出答案与解释，促进学生发现问题，同时老师也能发现学生的盲点，并能有针对性地进行后面的讲课。
三、知识讲解 知识点1：by + v.-ing结构是一个重点，该结构意思是“通过……，以……的方式”，后面常接v.-ing 形式，表示“通过某种方式得到某种结果”，即表示行为的方式或手段。 I practice speaking English by joining an English-language club. 我通过加入一个英语语言俱乐部来练习讲英语。 Mr Li makes a living by driving taxis.李先生靠开出租车为生。 介词by + v.-ing 结构常用来回答How do you...?或How can I...?之类的问题。 —How do you learn English? 你怎样学习英语呢？ —I learn English by reading aloud. 我通过大声朗读来学英语。 —How can I turn on the computer? 我怎样才能打开电脑呢？ —By pressing this button. 按这个按钮。
知识点2：by 是个常用介词，其他用法还有： 1【考查点】表示位置，意思是“在……旁边”，“靠近……”，有时可与beside互换。The girls are playing by (beside) the lake. 女孩们正在湖边玩。 此时要注意它与介词near有所不同，即by 表示的距离更“近”。比较： He lives by the sea. 他住在海滨。He lives near the sea. 他住在离海不远处。