10.1.1.109.5156 - WAVELET-BASED IMAGE PROCESSING To Berlina...

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WAVELET-BASED IMAGE PROCESSING To Berlina James S. Walker Department of Mathematics University of Wisconsin–Eau Claire [email protected] Abstract The 1990’s witnessed an explosion of wavelet-based methods in the field of image processing. This paper will focus primarily on wavelet-based image compression. We shall describe the connection between wavelets and vision and how wavelet techniques provide image compression al- gorithms that are clearly superior to the present jpeg standard. In particular the wavelet-based algorithms known as spiht , aswdr , and the new standard jpeg 2000 , will be described and compared. Our com- parison will show that, in many respects, aswdr is the best algorithm. Applications to denoising will also be briefly referenced and pointers supplied to other references on wavelet-based image processing. Keywords: Wavelets, Image Processing, Image Compression Introduction The field of image processing is a huge one. It encompasses, at the very least, the following areas: 1. Image Compression; 2. Image De- noising; 3. Image Enhancement; 4. Image Recognition; 5. Feature De- tection, 6. Texture Classification. Wavelet-based techniques apply to all of these topics. One reason that wavelet analysis provides such an all-encompassing tool for image processing is that a similar type of anal- ysis occurs in the human visual system. To be more precise, the human visual system performs hierarchical edge detection at multiple levels of resolution — and wavelet transforms perform a similar analysis (more on this below). Rather than attempting to describe in detail how wavelets apply to all of the areas listed above (that would take an entire book), we focus instead on the first topic, image compression. For those readers who desire to study Topic 2, image denoising, see [30], [29], [13], or [18]. 1
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2 Topics 3 to 5 are explained at an elementary level in [26], where further references can be found. Topic 6 is discussed in [9]. In this paper we shall provide a broad overview of image compression, especially highlighting a comparison between different image compres- sion algorithms. Mathematical details can be found in [30], [27], and [28], which are all available for downloading at the following webpage: http://www.uwec.edu/walkerjs/ISAAC2003/WBIP/ (1) The first part of the paper summarizes transform-based compression, including wavelet-based compression. 1 One type of transform-based compression is the block- dct 2 method used in the jpeg 3 algorithm. The jpeg algorithm (.jpg files) is widely used for sending images over the Internet and in digital photography. Wavelet-based algorithms out- perform the jpeg algorithm. The new jpeg algorithm, jpeg 2000 , uses a wavelet transform instead of a block- dct . Below we shall compare jpeg with jpeg 2000 and two other wavelet transform-based algorithms ( spiht 4 and aswdr 5 ). This comparison comprises the second part of our paper. Our comparison will show that, in many respects, aswdr is the best algorithm. It even outperforms jpeg 2000 .
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