Deconvolution of poissonian images via iterative shrinkage

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 measurement noise. In the field of optics and nuclear imaging, the noise is commonly assumed to obey a Poisson distribution. In this note, 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 convergence to the global maximizer of an associated maximum-a-posteriori criterion.