Statistics of transform coding and assessment of reconstructed image quality

Transform coding is an important data compression technology that is the basis for many industry image compression standards. This dissertation studies the statistics of transform coding and applies the statistics to model observers for assessing the quality of reconstructed medical images for diagnostic detection tasks. The research results provide a theoretical foundation for optimizing compression algorithms and assessing the reconstructed image/video quality.; The block-based image transform, in this study, is defined as a one-dimensional linear transform which mathematically reveals the intrinsic relationships among image blocks. It is shown that compression noise is a linear transform of quantization noise, which is usually generated during quantization of transform coefficients using multidimensional uniform scalar quantizers. The statistics of quantization and the statistics of transform coding are derived in this study. It shows that compression noise of transform coding has a Gaussian distribution. The statistics of transform coding are verified by using the JPEG compression algorithm and lumpy background images, which are widely used to simulate mammogram images. The theoretical results agree closely with the statistics of the actual compression data.; Model observers are algorithms to predict the performance of human observers for diagnostic detection tasks; some of them, especially the channelized Hotelling observers, have been used successfully in medical applications. By using the compression noise statistics in two-alternative force choice (2AFC) tests, several model observers applied to decompressed images are derived in analytical form; they are further approximated by using the statistics of decompressed background images without any knowledge of the detection objects. The derived model observer performance and its approximations are verified using various decompressed JPEG background images with circular or Gaussian signals. They closely agree with the actual calculated performance. The derived performance can be used to optimize quantization scheme, which in turn will help to compress medical images efficiently based on the nature of the specific diagnostic tasks.; In addition to the model observers, the statistics derived from this study can be used to optimize image/video compression algorithms, such as quantization algorithm optimization, artifact removal, compression noise reduction, etc. It also provides a theoretical foundation for reconstructed image/video quality assessments.