Analytical-form model observers for decompressed images

We report a method for evaluating the performance of model observers for decompressed images in analytical form using compression noise statistics. It derives test statistics and detectabilities for the ideal observer, the nonprewhitening observer, the Hotelling observer, and the channelized Hotelling observer (CHO) on decompressed images. The derived CHO performance is validated using the Joint Photographic Experts Group (JPEG) compression algorithm. The validation results show that the derived CHO receiver operating characteristics (ROCs) and areas under ROC curves predict accurately their corresponding estimated values. These analytical-form quality measures of decompressed images provide a way to optimize compression algorithms analytically, subject to a model-observer performance criterion. They also provide a theoretical foundation for efforts to create a model observer for decompressed images.