Wavelet transform image coding scheme is the widest used one ofimage 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.%小波变换编码是目前研究较多的图像压缩方法，变换系数的量化是获得低比特率、高信噪比压缩图像的关键步骤。为了设计最优量化器，必须确定变换系数的分布规律。选择“Face”、“Girl”、“Lena”和“Panda”4幅标准图像数据进行统计研究，用长度L=18的Vetterli双正交小波将256灰度级256×256图像分解为3层10个子带，使用“KS”测试统计方法确定图像小波变换系数的分布规律。给出了瑞利分布、高斯分布和拉普拉斯分布假设下的“KS”测试统计结果。统计结果表明，低频部分符合高斯分布，其余部分符合拉普拉斯分布。模拟结果显示，假设高频部分符合拉普拉斯分布可获得比高斯分布假设更高的恢复图像信噪比。
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