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This paper describes a multistage perceptual quality assessment (MPQA) model for compressed images. The motivation for the development of a perceptual quality assessment is to measure (in)visible differences between original and processed images. The MPQA produces visible distortion maps and quantitative error measures informed by considerations of the human visual system (HVS). Original and decompressed images are decomposed into different spatial frequency bands and orientations modeling the human cortex. Contrast errors are calculated for each frequency and orientation, and masked as a function of contrast sensitivity and background uncertainty. Spatially masked contrast error measurements are then made across frequency bands and orientations to produce a single perceptual distortion visibility map (PDVM). A perceptual quality rating (PQR) is calculated from the PDVM and transformed into a one to five scale, PQR 1-5, for direct comparison with the mean opinion score, generally used in subjective ratings. The proposed MPQA model is based on existing perceptual quality assessment models, while it is differentiated by the inclusion of contrast masking as a function of background uncertainty. A pilot study of clinical experiments on wavelet-compressed digital angiogram has been performed on a sample set of angiogram images to identify diagnostically acceptable reconstruction. Our results show that the PQR 1-5 of diagnostically acceptable lossy image reconstructions have better agreement with cardiologists' responses than objective error measurement methods, such as peak signal-to-noise ratio. A Perceptual thresholding and CSF-based Uniform quantization (PCU) method is also proposed using the vision models presented in this paper. The vision models are implemented in the thresholding and quantization stages of a compression algorithm and shown to produce improved compression ratio performance with less visible distortion than that of the embedded zerotrees - - wavelet (EZWs).