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Quantization in wavelet based image compression systems

Keywords:

A.L. Priorov, I.S. Mochalov


Most current digital image wavelet-compression systems based on the principle transform / quantization / entropy coding. Naturally at each step you want to achieve maximum gains. However, this approach does not always produce the best results, because modern compression algorithms (SPIHT, EBCOT, etc.) use a complex hierarchical structure entropy coding. The problem is that the adaptive quantization techniques based on the coding of transform coefficients as a random source. Mallat showed that coding coefficients as a random source is not effective way even when the decoder knows the probability density function of the source. Because of these problems, encoders (EZW, SPIHT, EBCOT) usually use simple scalar quantization with uniform quantization scale and extended zero level. There are better methods of vector quantization, requiring additional computing resources, but they do not solve this problem completely. Therefore, building a good quantization system must be based on the hierarchical structure of the entropy coder (eg, SPIHT). We must define the partition of the set of values into the set of intervals and code book, which will contain the values that are mapped to the i-th interval in the inverse quantization (dequantization). When the system is built, the quantization process scalar or vector value into index of interval, which holds the value. Entropy coder converted indices i into bitstream. Dequantization recover corresponding index value from the codebook. A natural requirement in the construction of the system is to minimize the quantization error whit constraints on the size of the bitstream. In this work new algorithm for the quantization of wavelet coefficients proposed. It minimize distortion in the wavelet-domain at a fixed codebook, bitstream size and entropy encoder STW (SPIHT). The results of testing the algorithm fully confirm the theoretical position. The algorithm was tested on a series of test images from the University of Southern California test database (http://sipi.usc.edu/database/). At all steps of quantization and on all test images from a database developed algorithm is superior quantization algorithm SPIHT on average of 0.5 – 1 dB PSNR metric. The basic algorithms of quantization of the wavelet coefficients in compression systems are considered. New wavelet coefficients quantization algorithm based on the hierarchical structure of the entropy coder which minimizes MSE of the wavelet coefficients with a fixed codebook and restrictions on the number of bits was offered.
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