Restoration of images with optical aberrations and quantization in a transform domain

Digital images generally suffer from two main sources of degradations. The first includes errors introduced in imaging, such as blurring due to optical aberrations and sensor noise. The second includes errors introduced during the processing. One particular example is the quantization noise arising from lossy compression. While image restoration is concerned with the recovery of the object from these degradations, often we only deal with one type of the error at a time. In this paper, we present a restoration algorithm that handles images with optical aberrations and quantization in a transform domain. We show that it can be cast in a joint optimization setting, and demonstrate how it can be solved efficiently through alternating minimization. We also prove analytically that the algorithm is globally convergent to a unique solution when the restoration uses either H-norm or TV -norm regularization. Simulation result asserts that this joint minimization produces images with smaller relative errors compared to a standard regularization model.