IMAGE COMPRESSION AND DENOISING BASED ON TREE – ADAPTED WAVELET SHRINKAGE Seminar

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ABSTRACT


An algorithm is described for simultaneously compressing and denoising images. The algorithm is called tree-adapted wavelet shrinkage and compression (TAWS-Comp). TAWS-Comp is a synthesis of an image compression algorithm, adaptively scanned wavelet difference reduction (ASWDR), and a denoising algorithm, tree-adapted wavelet shrink age (TAWS). As a Compression procedure, TAWS-Comp inherits all of the advantages of ASWDR: its ability to achieve a precise bit-rate assigned before compressing, its scalability of decompression, and its capability for enhancing regions-of interest. Such a full range of features has not been available with previous compressor plus denoiser algorithms. As a denoising procedure, TAWS-Comp is nearly as effective as TAWS alone. TAWS has been shown to have good performance, comparable to state of the art denoisers. In many cases, TAWS-Comp matches the performance of TAWS while simultaneously performing compression. TAWS-Comp is compared with other combined compressor/denoisers, in terms of error reduction and compressed bit-rates. Simultaneous compression and denoising is needed when images are acquired from a noisy source and storage or transmission capacity is severely limited (as in some video coding applications). An application is described where the features of TAWS-Comp as both compressor and denoiser are exploited.
Keywords: image compression; image denoising; signal processing; video coding.


1 . INTRODUCTION
We shall describe an algorithm for simultaneously compressing and denoising an image corrupted by additive random noise. The classical approach to compressing a noisy image—motivated by results from rate distortion theory [1], [2] — is to use a two-step process. In the first step, the noisy image is denoised, while in the second step the denoised image is compressed. There are situations, however, where limited processor resources call for the greater efficiency afforded by combining compressing with denoising. Combining compressing with denoising is particularly apt for situations, such as some video coding applications, that satisfy the following three conditions: (1) the image source is noisy, (2) the time for processing is short and/or processor power is limited, and (3) the transmission channel capacity is low. Condition (1) calls for denoising, condition (3) calls for compressing, and condition (2) calls for a simultaneous denoising and compressing in order to save time and/or free the processor for other tasks. From this point on, we shall refer to such a combined compressor plus denoiser as a compdenoiser. The paper is organized as follows. In section 2, we describe the TAWS method. This section begins with a brief summary of the compression method from which TAWS is derived. Understanding the

rationale behind this compression technique helps in understanding how TAWS combats the ringing artifacts that wavelet shrinkage suffers from. It also

helps in understanding how TAWS dynamically adapts the sizes of thresholds in relation to specific image features. In section 3, we report on denoisings of test images. A comparison of TAWS with various state of the art denoising methods is done in this section. The paper concludes in section 4 with a brief
discussion of future work.

2 . THE TAWS METHOD
The TAWS denoising method is built upon the ideas involved in a new lossy image codec called Adaptively Scanned Wavelet Difference Reduction (ASWDR), which is described in [1]. Here is a summary of this method, with some amendments made to adapt to the noise removal case:
Step 1. Perform a wavelet transform of the discrete image, {f [i, j]}, producing the transformed image, {f [i, j]}, for the denoising reported on in this paper, the Daub 9/7 transform [5] was used exclusively.
Step 2. Use a scanning order for searching through the transformed image. This is a one -to- one and onto mapping {f [i, j]} =x[k], whereby the transform values are scanned through via linear ordering k=1, 2…, M. The value of M being the number of pixels in the image. Initially, the scanning order is a zigzag through sub bands, from lower to higher [6].
Step 3. Choose an initial threshold, T, such that at least one transform value x[n] say, satisfies | x[n] | = T, and all transform values, x[k],satisfy | x[k] | < 2T.
Step 4 (Significance pass). Determine new significant index values—i.e., those new indices m for which x[m] has a magnitude greater than or equal to the present threshold. Assign a value q[m]= Tsign(x[m]) as the quantized value corresponding to the transform value x[m].
Step 5 (Refinement pass). Refine quantized
transform values corresponding to old significant transform values. Each refined value is a better approximation to the exact transform value. More details of this step will be provided below.