Closed-form compression noise in images with known statistics
Dunling Li, Murray H. Loew · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
This paper studies the principle of transform coding and identifies the quantization noise as the sole distortion. It shows that compression noise is a linear transform of quantization noise, which is usually generated during quantization of transform coefficients using uniform scalar quantizers. The quantization noise may not distribute uniformly as distributions and quantization step sizes vary among transform coefficients. This paper derives the marginal, pairwise and joint probability density functions (pdfs) of multi-dimensional quantization noise. It also shows the mean vector and covariance matrix of quantization noise in closed-form. Based on above results, this paper derives closed-form compression noise statistics, which include marginal pdfs, pairwise pdfs and joint pdf, mean vector and covariance matrix of compression noise. This paper shows compression noise has a jointly normal distribution, which enables its calculation to have reasonable computation complexity. The derived statistics of quantization and compression noise are verified by using the JPEG compression algorithm and lumpy background images. Verification results show that derived statistics closely predicts estimated ones. This paper provides a theoretical foundation to derive closed-form model observers and to define closed-form quality measures for compressed medical images.