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Image compression through wavelet transform coding

机译：小波变换编码的图像压缩

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摘要

A novel theory is introduced for analyzing image compression methods that are based on compression of wavelet decompositions. This theory precisely relates (a) the rate of decay in the error between the original image and the compressed image as the size of the compressed image representation increases (i.e., as the amount of compression decreases) to (b) the smoothness of the image in certain smoothness classes called Besov spaces. Within this theory, the error incurred by the quantization of wavelet transform coefficients is explained. Several compression algorithms based on piecewise constant approximations are analyzed in some detail. It is shown that, if pictures can be characterized by their membership in the smoothness classes considered, then wavelet-based methods are near-optimal within a larger class of stable transform-based, nonlinear methods of image compression. Based on previous experimental research it is argued that in most instances the error incurred in image compression should be measured in the integral sense instead of the mean-square sense.
机译：引入了一种新颖的理论来分析基于小波分解压缩的图像压缩方法。该理论与（a）原始图像和压缩图像之间的误差的衰减率随着压缩图像表示尺寸的增加（即，随着压缩量的减小）有关，与（b）图像的平滑度相关。在某些称为Besov空间的光滑度类中。在该理论内，解释了小波变换系数量化所引起的误差。详细分析了基于分段常数近似的几种压缩算法。结果表明，如果图片可以通过其在所考虑的平滑度类别中的隶属关系来表征，则基于小波的方法在较大的一类稳定的基于变换的非线性图像压缩方法中几乎是最佳的。根据先前的实验研究，认为在大多数情况下，图像压缩中产生的误差应以积分意义而不是均方意义来衡量。

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