IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Retrieving Image from Noisy Version depending on Multiwavelet Soft-Thresholding with Smo othing Filter S. A. Fahdel Departme nt of Computer Science, College of Education Ibn-Al-Haitham, Unive rsity ofBaghdad Abstract In this p aper, we describe a new method for image denoising. We analyze p rop erties of the M ultiwavelet coefficients of natural images. Also it suggests a method for comp uting the M ultiwavelet transform using the 1 st order approximation. This p aper describes a simple and effective model for noise removal through suggesting a new technique for retrieving the image by allowin g us t o estimate it from the noisy image. The p rop osed algorithm depends on mixing both soft -thresholds with M ean filter and apply ing concurrently on noisy image by dividing into blo cks of equal size (for concurrent p rocessed to increase the p erformance of the enhancement p rocess and to decease the time that is needed for imp lementation by app ly ing the p rop osed algorithm on all four blocks concurrently ) which are emp loy ed in order to remove the noise. The p rop osed method of image retrieving and smoothing outp erforms the conventional methods t hat are used for image enh ancement. The su ggested al gorithm and the evaluation test carried usin g Delphi V.5 p ackage. Introduction Digital ima ges are p ronr to a v ariety of typ es of noise. Noise is the r esult of errors in the image acquisition p rocess that result in p ixel values t hat do not reflect the true intensities of the real sc ene. There are several way s that noise can be introduced into an ima ge, d epending on how t he image is created . For e xamp le [1], if the image is scanned from a photograph made on film, the film grain is a source of noise. Noise can also be the result of damage to t he film, or b e introduced by the scanner itself. Also, if the image is acqu ired directly in a digital for mat, the mechan ism for gathering the data (such as a CCD detector) can introduce noise, and electronic transmission of image data can introduce noise. In p ractice, image d enoisin g is used when y ou somehow obtain a noisy image, and y ou want to remove as many of the sp eckles from the image as p ossible, without removing or distorting any features in it. Both denoising and enhancement are imp ortant field in digital image p rocessing. Transforms p lay a great ro le in this field since they offer a new representation for the data in which features to be processed become more distinct [2]. There are two p owerful techniques to reduce the noise lev el in a si gn al:- M ean filterin g and M ultiwavelet Soft-Thresholding. M ean filterin g is a lin ear p rocedure while M ultiwavelet Soft-Thresholding is nonlinear. Classical versions of both methods tend to blur edges in images. We try to blend these two approaches in order to imp rove the p erformance. Our idea is to divide the input image (no isy version) into four blocks of equal size then app ly M ultiwavelet Soft-Thresholding for each distinct block and the result that achieved from this st ep will be enh anced by using M ean filter, then group the four dist inct resultant blocks t o get the final retrieval image. M ultiwavelet transformation is directly app licable only to one- dimensional si gnals, but images are two-dimensional signals, so there must be a way to IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 p rocess them with a one-dimensional transform [1]. The next section will describ e how to make this t yp e of transformation to work with images. Types of Thresholding and its Selection Rules:- Thresholding is non-linear operation p erformed on the M ultiwavelet coefficients of noisy signal [5]. It is widely used in noise reduction, signal and image comp ression or recogn ition [3]. This can be done by comp aring the absolute value of the emp irical M ultiwavelet coefficients with a value called Threshold Value (Thv). It is clear that if the M ultiwavelet coefficient is equal to or less than the threshold valu e, then one can not sep arate the signal from the noise. In this case, a good estimation for that M ultiwavelet coefficient is zero. In the case of an emp irical M ultiwavelet coefficient is greater than the threshold value, then a natural estimation for this M ultiwavelet coefficient is emp irical M ultiwavelet coefficient itself. This idea is called Thresholding. 2.1 Hard-Thresholding:- Which can be computed by [5]:- Whe re Thv is the threshold value or the gate value. 2.2 Soft-Thresholding:- Can be comp uted as [8]:- ______ (1)           Thv j k G Thv j k G j k G Thv), j k (G h T j k A 0 ˆ            01 00 01 -: j k G j k G j k G j k (G Sign Where ) ______ (2)           Thv j k G Thv j k GThv j k G j k (G Sign Thv), j k (G h T j k A 0 ) ˆ IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 The graphical representation for the two types of Thresholding (Hard and Soft Threshloding) is shown in figures (1 and 2 resp ectively). Threshold Selection Rules:- In Thresholding p rocess, coefficients smaller than threshold value Thv are judged negligible, or noise other than signal. Hence, threshold value Thv controls the degree of noise rejection, but also of valid signal rejection. One hop es, to set thresholds which are small, but which are very likely to exceed every coefficient in case of a p ure noise signal [3, 5]. Two rules are used to select threshold values as follows:-  Select t he threshold by estimating the standard deviation zσ of the noise at each scale, and takin g into account that the threshold values have to be differ ent on each scale level. The thresholds in this case are calculated as zσbThv  where b is a p arameter, typically between 2 and 4.  The choice of the threshold is a very delicate and imp ortant statistical p roblem. A b ig threshold Thv leads to a large bias of the estimator. On the other hand, a small threshold increases the variance of the smoother. Donoho and Johnstone have p rop osed the following v alue of the suitable value of threshold:- A proposed algorithm for retrieving image from noisy version depending on Multiwavelet Soft-Thresholding with using equal size block divide with me an filte In this section, new method is p rop osed for retrieving image from noisy version by dividing the noisy image into four equal size blocks and usin g M ultiwavelet Soft- Thresholding then enhances the result through an enhancement filter of type mean filter which is applied two times on some p arts of the p rocessed image, as shown in the figur e (2).The step s of the p rop osed method are as follows:- 1. Divide the input noisy image into four blocks of equal size, and then obtain the M ultiwavelet transformation coefficients )( jkG for the four divided blocks concurrently . 2. Compute the threshold value (Thv) by equation (3) or any other one of the threshold selection rules mentioned in p revious section (2.3) then filter the M ultiwavelet transform coefficients )( jkG by equation (2) which is used to comp ute the Soft- Thresholding since the work of this research depends on the Soft- Thresholding typ e, then replace the M ultiwavelet transform coeff icients )( jkG by applying the si gn function on it and multip ly the result by the absolute value of the coefficients then subt ract the value of Thv fro m the final r esult if the absolute value for M ultiwavelet transform coefficients )( jkG is greater than the threshold value (Thv), else replace it with a zero value. 3. App ly enhancement app roach on the high p ass region for each resultant by using mean filter and leave the low-p ass components as it is. 4. Inverse the M ultiwavelet transform threshold coefficients )( jk to retrieve the image, and smooth each resultant block by using mean filter, then group the resultant four ______ (3) si gnal .input the of length the is Whe re ))(2( N N e log z σSqrtThv 2 IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 blocks with each other to form the denoised smoothing ima ge which r epresents the final result from this algor ithm. Figure (3) shows the block diagr am for this p rop osed algorithm. Syste m Implementation and Re quireme nts The sy stem is design ed by dividing into four main p arts:- 1. Dividin g the noisy image into four blocks, as shown in figure (4.A.1). 2. M ultiwavelet transforms and it's inverse, as shown in figure (4.A.2 and 4.B.1). 3. Computing Soft-Thresholding values, as shown in figure (4.A.3). 4. Smoothin g filter which is app lied two times, as shown in figure (4.A.3 and 4.B.2). By using the sp ecified sy stem requirements, figur es (4.A and 4.B) will illust rate how the suggested algorithm has been work Here is t he table of valu es for comp arin g between the initial noisy image and the r esultant final enhanced image to imp rove the efficiency of the prop osed algorithm, note that the value of SNR (Sign al to Noise Ratio) is comp uted using the following equation:- Where:-  crI ,ˆ Represents the signal (The Denoised I mage) with r-row of size equal to M and c- column of size equal to N.  crX , Represent t he errors (The Noisy Image) with r-row of size equal to M and c-column of size equal to N. Not e that the large numb er for the value of SNR means we get a bett er image Conclusions This p aper p resents a new t echnique for image denoisin g throu gh the use of M ultiwavelet Soft-Thresholding. Using this method, ima ge noise can be reduced effectively and litt le image detail is lost. M ultiwavelet transform have a great and imp ortant role in image denoising and enhancement due to its multi-resolution analy sis. It dep ends on the same principles of wavelet transform with different two-dimensional filters and with p re/p ost p rocessing mechan isms. From the work in this p ap er, the following p oints are concluded :- 1. Dividin g image into blocks of equal size not for i mproving the enh ancement p rocess but to imp rove the p erformance of the algor ithm by reducing the time of p rocessing. The purp ose from dividin g the image into four blo cks of equal sizes is to concurr ent p rocessed in order to incr ease the p erformance of the enhancement p rocess and to decease the time that is needed for imp lementation by apply ing the p rop osed algorithm on all four blocks concurrently (at the same time). This will led to reduce the time of imp lementation to a rate equal the numb er of blocks, i.e., if the image is divided into 16 blocks of equals size, the time needed to p erform this algorithm is reduced to t he number of blocks which is here 8 units of time. 2. By comp uting the value of SNR we can conclude that the value of SNR for t he noisy image (Initial Noisy Image) is equal to 0.0783, this value is the same for each b lock after dividing p rocess, while this value will be 3.0938 and the same for each block after applying the prop osed algor ithm. This will led to show that the value of SNR ______ (4)                                     1 0 1 0 2 1 0 1 0 2 10 ,, ,ˆ log10 M r N c M r N c crcrX crI SNR IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 3. could not be chan ged dependin g on d ividing b locks and the p roof for this is SNR st ill have the same valu e, but SNR will be chan ged after app ly ing the algor ithm and table (1) shows that. 4. Sever al p apers and researches d eal with wavelet t ransformation that is used in image denoisin g and comp ression due to the prop erties of this transform. These prop erties are orthogonality , comp act supp ort, linear p hase, and high approximation/vanishin g moments of the basis function, are found to be usefu l in image p rocessing techniques. Unfort unately, the wavelets can never p ossess all the above mentioned p rop erties simultaneously M ultiwavelet p ossesses more than one scaling functio n offer the p ossibility of sup erior p erformance and high degree of freedom for ima ge p rocessing app lications, comp ared with scalar wavelets. M ultiwavelet can achieve bett er level of p erformance than scalar wavelets with similar comp utational comp lexity . Dealing with image denoisin g usin g M ultiwavelet transform, gives an idea that M ultiwavelet eliminates the no ise from ima ges bett er than usin g th e wavelet t ransform. 5. There are two imp ortant p arameters in M ultiwavelet Thresholding denois ing algorithm namely the threshold valu e (Thv) and the M ultiwavelet basis. For the first p arameter, it is found that the op timal threshold value can be comp uted as bz, where b is a constant. Re ferences 1. Strang, G. and Strela, V. (1995), Short Wavelets and M atrix Dilation Equations, IEEE Trans. Sign al Proccessing, 43, 108-115. 2. Strela, V. (1996).M ultiwavelet: Theory and App lications Transforms, Ph.D. thesis, Dep . Of M ath., M assachusetts Institute of Technology , June 3. M ohammed, Z. J. (2004). Video I mage Compression Based on M ultiwavelet Transforms, University of Baghdad, Computer Science and Information Sy st em Dep . 4. Saleh, Z. J. M . (2004), Image Video Compression Using Multi-Wavelet Transform, Ph.D Thesis, University of Baghdad, Baghd ad. 5. Donoho, D. (1995), De-noising by soft -thresholding, I EEE Trans. on Info. Theory, 43, 613–627. 6. Xia, X.-G., Geronimo, J. S. Hardin, D. P., and Suter, B. W. (1995), On Computations of M ultiwavelet T ransforms, Proc. SPIE, pp .27-38. 7. Hadi, A. H (2004), Wavelet-Domain Reconstruction of Lost Blocks in Image,” M .Sc. Thesis, University of Technology , Baghd ad. 8. Taubman, D. and M arcellin, M . (2002), “JPEG 2000 Image Co mpression, Fundamentals, Standards, and Practice”, Kluwer Aczdemic Publishers, 1st edition. 9. Alkachouch, Z. and Bellanger, M . (2000), Fast DCT-Based Sp atial Domain Interpolation of Blocks in Images, IEEE Transactions on Image Proc essing, 9 (4): 729–732. 10. LU,Y. DO, M . N. A.(2005). Directional Extension for M ultidimensional Wav elet Transforms, EEE Transactions on Image Processin g, submitt ed; 11. Wan g Lin g, (2000). Ort hogon al M ultiwavelet Transform for Image Denoising”, Proceedings of ICSP2000, p p . 987-991, IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Ini tial Noi sy Image Block1 Block2 Block3 Block4 Final Enhanced Image Size H =256 W = 256 H = 64 W = 64 H = 64 W = 64 H = 64 W = 64 H = 64 W = 64 H = 256 W = 256 SNR before app lying algorithm 0.0783 0.0783 0.0783 0.0783 0.0783 SNR after app lying algorithm 3.0938 3.0938 3.0938 3.0938 3.0938 Th e difference between the results Th e difference b etween the results can b e comuted by 3.0938 - 0.0783 = 3.0155 (Three times of the denoisin g degree). Th at means the advan tage of this algorithim is to get a greate value for SNR which leds to get b etter image. Th e Time needed for the processing Th e same for all since these b locks are runn ing concurrently (at the same time), so the time n eeded for implementation is redu ced to the f our times (the nu mber of blocks) that is is n eeded when process the image without dividing. Fig. (1) Hard Threshol ding Fig. (2) Soft Threshol di ng Table (1):- Comparing between the results before and after applying the algorithm IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Fig. (3) A flow diagram for the propose d image retrieving method by using Multiwavelet Soft-Thresholding with enhancement mean filte r Mul tiwavel et Coefficients Noisy Input Image Divided to four bl ocks Smooth high-pass components with mean fil ter Compute Thv usi ng ))(2( NlogσSqrtThv e 2 z Filter the Coefficients usi ng Soft-Threshol d DMWT IDMWT Group the four blocks Smoothing the resultant blocks with mean fil ter The retrieval enhanced final image IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Noisy Input Image 2- Comput e MWT for each block Block no.4 Block no.3 Block no.2 Block no.1 1- Divided the noisy i mage into four equal size bl ocks Block no.4 Block no.2 Block no.1 Block no.3 Fig. (4.A) A step by step i mpl ementation for image retrieving method by usi ng Mul tiwavel et Soft-Threshol di ng with smoothing mean filter Block no.4 Block no.3 Block no.2 Block no.1 3- Fil tering with Smoothing IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.23 (2) 2010 Fig. (4.B) The reminder step by step impl ementation for image retrievi ng method by using Mul tiwavel et Soft-Threshol di ng with smoothing mean fil ter. Block no.4 Block no.3 1- Comput e ID MWT Coeff icients for each resul tant block Block no.2 Block no.1 Block no.4 Block no.3 2- Smooth each resultant block by usi ng mean fil ter Block no.2 Block no.1 3- Group the four blocks IHJPAS مع Soft-Thesholdingمن النسخة المشوهة باستخدام استرجاع الصور تحویل متعدد المویجة شیماء عباس فاضل جامعة بغداد ،أبن الهیثم –كلیة التربیة ، قسم علوم الحاسبات الخالصة ویل متعدد یقترح هذا البحث طریقة السترجاع وازالة التشویه من الصور الملونة وتحسینها من خالل استخدام تح عن طریق االستفادة من الخصائص الممكن الحصول علیها من ) Discrete Multiwavelet Transform(المویجة .خالل تطبیق هذا النوع من التحویالت 1(طریقة لكیفیة حساب نوع من انواع تحویالت متعدد المویجة الذي یعرف بالنظام التقریبي االول ایضاً یقترح هذا البحث st Order Approximation .( ح ویوضح هذا البحث طریقة مبسطة وذا فاعلیة في ازالة التشویه من الصور من خالل اقترا -Soft(الخوارزمیة التي تم اقتراحها في هذا البحث تعتمد على مزج كل من . تقنیة جدیدة السترجاع الصور Thresholding ( مع)Mean Filter (ة باالعتماد على تحویل متعدد المویج)Discrete Multiwavelet Transform DM WT (ء علىیتم تطبیقها بشكل متزامن على الصورة عن طریق تقسیم وتجزئة الصورة اذ اربعة اجزا وتتم معالجة كل جزء بشكل انفرادي ومتزامن مع االجزاء االخرى ) Equal Size Block Divide(متساویة االحجام ان . رعة المعالجة في ازالة وتحسین الصور الملونة وبشكل متزامن لكل اجزاء الصورةوالغرض من هذا التقسیم هو لزیادة س ق التقلیدیة المستخدمة والمتعارف علیها في ائالطریقة المقترحة في عملیة استرجاع وازالة التشویه والتحسین تفوق الطر .عملیات تحسین الصور الملونة Delphi V.5(ذا البحث من خالل استخدام لغة باسكال المرئیة المعروفة بـ تم تقییم الخوارزمیة التي تم اقتراحها في ه Package (االصدار الخامس يذ. 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