Iterative Shrinkage Approach to Restoration of Optical Imagery

The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the resolution limitations of an imaging device in use and/or by the destructive influence of measurement noise. Specifically, when the noise obeys a Poisson probability law, standard approaches to the problem of image reconstruction are based on using fixed-point algorithms which follow the methodology first proposed by Richardson and Lucy. The practice of using these methods, however, shows that their convergence properties tend to deteriorate at relatively high noise levels. Accordingly, in the present paper, a novel method for de-noising and/or de-blurring of digital images corrupted by Poisson noise is introduced. The proposed method is derived under the assumption that the image of interest can be sparsely represented in the domain of a linear transform. Consequently, a shrinkage-based iterative procedure is proposed, which guarantees the solution to converge to the global maximizer of an associated maximum-a-posteriori criterion. It is shown in a series of both computer-simulated and real-life experiments that the proposed method outperforms a number of existing alternatives in terms of stability, precision, and computational efficiency.