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On the distribution tests of the two-dimensional wavelet transform coefficients for image

ZHANG Qi zhi (Department Computer Science & Automation,Beijing Institute of Machinery, Beijing 100085, China)  
Wavelet transform image coding scheme is the widest used one of image compression approaches. The quantization of wavelet transform coefficients is a key to obtain the compression image with low bit ratios and the reconstruction image with high signal to noise ratio. To obtain the optimal quantizer,the distributions of wavelet transform coefficients for image must be determined. The purpose of the experiment is to determine the distributions of wavelet transform coefficients for image. Four standard images, named “Face”, “Girl”, “Lena” and “Panda”, are selected to study the distribution rule. The “KS” statistical tests are applied to studying the distributions of wavelet transform coefficients for images. Utilizing the Vetterli biorthogonal wavelet ( L =18), the images that have size of 256×256 pels with 256 gray levels are decomposed to three level and ten subimages. The results of tests of Rayleigh assumption, Laplacian assumption and Gaussian assumption are given. The results of tests have shown that the low pass subimages are best approximated by a Gaussian distribution and the others are best approximated by a Laplacian distribution. A simulation indicates that the Laplacian assumption of coefficients yields a higher actual output signal to noise ratio than the Gaussian assumption.
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