Error Inhomogeneity in Wavelet-Based Compression

Despite the popularity of wavelet-based image compression, its shortcoming of having error inhomogeneity (EI), namely the error that is different for even and odd pixel location, has not been previously analyzed and formally addressed. The difference can be substantial, up to 3.4-dB peak signal-to-noise ratio (PSNR) for some images and compression ratios. In this paper, we show that the EI is caused by asymmetrical filtering of quantization errors after the upsampling step in wavelet synthesis process. Nonuniformity and correlation of quantization errors can also contribute to this EI, albeit to a smaller degree. In addition to explaining the source of EI, the model we developed in this paper also allows predicting its amount for a given wavelet. Furthermore, we show how to redesign wavelet filters to reduce this EI at a cost of a small reduction in the overall PSNR performance. For applications that are sensitive to PSNR degradation, we also show how to design wavelet filters that can gradually tradeoff PSNR performance for reduced EI.