IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 Retrieving Image from Noisy Version depending on Multiwavelet Soft-Thresholding with Smoothing Filter S. A. Fahdel Department of Computer Science, College of Education Ibn-Al-Haitham, University ofBaghdad Abstract In this paper, we describe a new method for image denoising. We analyze properties of the Multiwavelet coefficients of natural images. Also it suggests a method for computing the Multiwavelet transform using the 1 st order approximation. This paper describes a simple and effective model for noise removal through suggesting a new technique for retrieving the image by allowing us to estimate it from the noisy image. The proposed algorithm depends on mixing both soft-thresholds with Mean filter and applying concurrently on noisy image by dividing into blocks of equal size (for concurrent processed to increase the performance of the enhancement process and to decease the time that is needed for implementation by applying the proposed algorithm on all four blocks concurrently) which are employed in order to remove the noise. The proposed method of image retrieving and smoothing outperforms the conventional methods that are used for image enhancement. The suggested algorithm and the evaluation test carried using Delphi V.5 package. Introduction Digital images are pronr to a variety of types of noise. Noise is the result of errors in the image acquisition process that result in pixel values that do not reflect the true intensities of the real scene. There are several ways that noise can be introduced into an image, depending on how the image is created . For example [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 the film, or be introduced by the scanner itself. Also, if the image is acquired directly in a digital format, the mechanism for gathering the data (such as a CCD detector) can introduce noise, and electronic transmission of image data can introduce noise. In practice, image denoising is used when you somehow obtain a noisy image, and you want to remove as many of the speckles from the image as possible, without removing or distorting any features in it. Both denoising and enhancement are important field in digital image processing. Transforms play a great role 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 powerful techniques to reduce the noise level in a signal:- Mean filtering and Multiwavelet Soft-Thresholding. Mean filtering is a linear procedure while Multiwavelet 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 improve the performance. Our idea is to divide the input image (noisy version) into four blocks of equal size then apply Multiwavelet Soft-Thresholding for each distinct block and the result that achieved from this step will be enhanced by using Mean filter, then group the four distinct resultant blocks to get the final retrieval image. Multiwavelet transformation is directly applicable only to one- dimensional signals, but images are two-dimensional signals, so there must be a way to IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 process them with a one-dimensional transform [1]. The next section will describe how to make this type of transformation to work with images. Types of Thresholding and its Selection Rules:- Thresholding is non-linear operation performed on the Multiwavelet coefficients of noisy signal [5]. It is widely used in noise reduction, signal and image compression or recognition [3]. This can be done by comparing the absolute value of the empirical Multiwavelet coefficients with a value called Threshold Value (Thv). It is clear that if the Multiwavelet coefficient is equal to or less than the threshold value, then one can not separate the signal from the noise. In this case, a good estimation for that M ultiwavelet coefficient is zero. In the case of an empirical Multiwavelet coefficient is greater than the threshold value, then a natural estimation for this Multiwavelet coefficient is empirical Multiwavelet coefficient itself. This idea is called Thresholding. 2.1 Hard-Thresholding:- Which can be computed by [5]:- Where Thv is the threshold value or the gate value. 2.2 Soft-Thresholding:- Can be computed as [8]:- ______ (1)           Thvj kG Thvj kGj kG Thv), j k(GhT j kA 0 ˆ            01 00 01 -: j kG j kG j kG j k(G Sign Where ) ______ (2)           Thv j kG Thv j kGThv j kG j k(G Sign Thv), j k(GhT j kA 0 ) ˆ IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 The graphical representation for the two types of Thresholding (Hard and Soft Threshloding) is shown in figures (1 and 2 respectively). Threshold Selection Rules:- In Thresholding process, 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 hopes, to set thresholds which are small, but which are very likely to exceed every coefficient in case of a pure noise signal [3, 5]. Two rules are used to select threshold values as follows:-  Select the threshold by estimating the standard deviation zσ of the noise at each scale, and taking into account that the threshold values have to be different on each scale level. The thresholds in this case are calculated as zσbThv  where b is a parameter, typically between 2 and 4.  The choice of the threshold is a very delicate and important statistical problem. A big 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 proposed the following value 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 mean filte In this section, new method is proposed for retrieving image from noisy version by dividing the noisy image into four equal size blocks and using Multiwavelet Soft- Thresholding then enhances the result through an enhancement filter of type mean filter which is applied two times on some parts of the processed image, as shown in the figure (2).The steps of the proposed method are as follows:- 1. Divide the input noisy image into four blocks of equal size, and then obtain the Multiwavelet transformation coefficients )( j kG 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 previous section (2.3) then filter the Multiwavelet transform coefficients )( j kG by equation (2) which is used to compute the Soft- Thresholding since the work of this research depends on the Soft- Thresholding type, then replace the Multiwavelet transform coefficients )( j kG by applying the sign function on it and multiply the result by the absolute value of the coefficients then subtract the value of Thv from the final result if the absolute value for Multiwavelet transform coefficients )( j kG is greater than the threshold value (Thv), else replace it with a zero value. 3. Apply enhancement approach on the high pass region for each resultant by using mean filter and leave the low-pass components as it is. 4. Inverse the Multiwavelet transform threshold coefficients )( j k to retrieve the image, and smooth each resultant block by using mean filter, then group the resultant four ______ (3) signal.input the of length the is Where ))(2( N N e log z σSqrtThv 2 IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 blocks with each other to form the denoised smoothing image which represents the final result from this algorithm. Figure (3) shows the block diagram for this proposed algorithm. System Implementation and Requirements The system is designed by dividing into four main parts:- 1. Dividing the noisy image into four blocks, as shown in figure (4.A.1). 2. Multiwavelet 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. Smoothing filter which is applied two times, as shown in figure (4.A.3 and 4.B.2). By using the specified system requirements, figures (4.A and 4.B) will illustrate how the suggested algorithm has been work Here is the table of values for comparing between the initial noisy image and the resultant final enhanced image to improve the efficiency of the proposed algorithm, note that the value of SNR (Signal to Noise Ratio) is computed using the following equation:- Where:-  crI ,ˆ Represents the signal (The Denoised Image) with r-row of size equal to M and c- column of size equal to N.  crX , Represent the errors (The Noisy Image) with r-row of size equal to M and c-column of size equal to N. Note that the large number for the value of SNR means we get a better image Conclusions This paper presents a new technique for image denoising through the use of Multiwavelet Soft-Thresholding. Using this method, image noise can be reduced effectively and little image detail is lost. Multiwavelet transform have a great and important role in image denoising and enhancement due to its multi-resolution analysis. It depends on the same principles of wavelet transform with different two-dimensional filters and with pre/post processing mechanisms. From the work in this paper, the following points are concluded:- 1. Dividing image into blocks of equal size not for improving the enhancement process but to improve the performance of the algorithm by reducing the time of p rocessing. The purpose from dividing the image into four blocks of equal sizes is to concurrent processed in order to increase the performance of the enhancement process and to decease the time that is needed for implementation by applying the proposed algorithm on all four blocks concurrently (at the same time). This will led to reduce the time of implementation to a rate equal the number of blocks, i.e., if the image is divided into 16 blocks of equals size, the time needed to perform this algorithm is reduced to the number of blocks which is here 8 units of time. 2. By computing the value of SNR we can conclude that the value of SNR for the noisy image (Initial Noisy Image) is equal to 0.0783, this value is the same for each block after dividing process, while this value will be 3.0938 and the same for each block after applying the proposed algorithm. 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. SCI. VOL.23 (2) 2010 3. could not be changed depending on dividing blocks and the proof for this is SNR still have the same value, but SNR will be changed after applying the algorithm and table (1) shows that. 4. Several papers and researches deal with wavelet transformation that is used in image denoising and compression due to the properties of this transform. These properties are orthogonality, compact support, linear phase, and high approximation/vanishin g moments of the basis function, are found to be useful in image processing techniques. Unfortunately, the wavelets can never possess all the above mentioned properties simultaneously Multiwavelet possesses more than one scaling function offer the possibility of superior performance and high degree of freedom for image processing applications, compared with scalar wavelets. Multiwavelet can achieve better level of performance than scalar wavelets with similar computational complexity . Dealing with image denoising using Multiwavelet transform, gives an idea that Multiwavelet eliminates the noise from images better than using the wavelet transform. 5. There are two important parameters in Multiwavelet Thresholding denois ing algorithm namely the threshold value (Thv) and the Multiwavelet basis. For the first parameter, it is found that the optimal threshold value can be computed as bz, where b is a constant. References 1. Strang, G. and Strela, V. (1995), Short Wavelets and Matrix Dilation Equations, IEEE Trans. Signal Proccessing, 43, 108-115. 2. Strela, V. (1996).Multiwavelet: Theory and Applications Transforms, Ph.D. thesis, Dep. Of Math., Massachusetts Institute of Technology, June 3. Mohammed, Z. J. (2004). Video Image Compression Based on Multiwavelet Transforms, University of Baghdad, Computer Science and Information System Dep. 4. Saleh, Z. J. M . (2004), Image Video Compression Using Multi-Wavelet Transform, Ph.D Thesis, University of Baghdad, Baghdad. 5. Donoho, D. (1995), De-noising by soft-thresholding, IEEE 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 Multiwavelet Transforms, Proc. SPIE, pp.27-38. 7. Hadi, A. H (2004), Wavelet-Domain Reconstruction of Lost Blocks in Image,” M.Sc. Thesis, University of Technology, Baghdad. 8. Taubman, D. and Marcellin, M. (2002), “JPEG 2000 Image Compression, Fundamentals, Standards, and Practice”, Kluwer Aczdemic Publishers, 1st edition. 9. Alkachouch, Z. and Bellanger, M. (2000), Fast DCT-Based Spatial Domain Interpolation of Blocks in Images, IEEE Transactions on Image Processing, 9 (4): 729–732. 10. LU,Y. DO, M. N. A.(2005). Directional Extension for Multidimensional Wavelet Transforms, EEE Transactions on Image Processing, submitted; 11. Wang Ling, (2000). Orthogonal Multiwavelet Transform for Image Denoising”, Proceedings of ICSP2000, pp. 987-991, IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 Initial Noisy 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 applying algorithm 0.0783 0.0783 0.0783 0.0783 0.0783 SNR after applying algorithm 3.0938 3.0938 3.0938 3.0938 3.0938 The difference between the results The difference between the results can be comuted by 3.0938 - 0.0783 = 3.0155 (Three times of the denoising degree). That means the advantage of this algorithim is to get a greate value for SNR which leds to get better image. The Time needed for the processing The same for all since these blocks are running concurrently (at the same time), so the time needed for implementation is reduced to the four times (the number of blocks) that is is needed when process the image without dividing. Fig. (1) Hard Thresholding Fig. (2) Soft Thresholding Table (1):- Comparing between the results before and after applying the algorithm IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 Fig. (3) A flow diagram for the proposed image retrieving method by using Multiwavelet Soft-Thresholding with enhancement mean filter Multiwavelet Coefficients Noisy Input Image Divided to four blocks Smooth high-pass components with mean filter Compute Thv using ))(2( NlogσSqrtThv e 2 z Filter the Coefficients using Soft-Threshold DMWT IDMWT Group the four blocks Smoothing the resultant blocks with mean filter The retrieval enhanced final image IHJPAS IBN AL- HAITHAM J. FOR PURE & APPL. SCI. VOL.23 (2) 2010 Noisy Input Image 2- Compute MWT for each block Block no.4 Block no.3 Block no.2 Block no.1 1- Divided the noisy image into four equal size blocks Block no.4 Block no.2 Block no.1 Block no.3 Fig. (4.A) A step by step i mplementation for image retrieving method by using Multiwavelet Soft-Thresholding 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. SCI. VOL.23 (2) 2010 Fig. (4.B) The reminder step by step implementation for image retrieving method by using Multiwavelet Soft-Thresholding with smoothing mean filter. Block no.4 Block no.3 1- Compute IDMWT Coefficients for each resultant block Block no.2 Block no.1 Block no.4 Block no.3 2- Smooth each resultant block by using mean filter 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 DMWT (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 زالة وتحسین الصور الملونة وبشكل متزامن لكل اجزاء الصورةوالغرض من هذا التقسیم هو لزیادة س ان . رعة المعالجة في ا 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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