Restoration of a Poisson distributed image using a principle of extreme physical information

Suppose that an object which reflects or emits light is captured by a sensor. The image data are distorted in various ways. The aim is to restore the object. For this purpose, a new restoration method is devised. It uses the Fisher-information based principle of extreme physical information (EPI). This solves a variational problem I − J = extremum, expressing a flow of information J → I from source to output in the restoration problem. Here, the source of information is the Poissonian image data, and J is modeled as its Hartley information level. Also, I is the Fisher information in the output restored object. The approach dates from the 1980s. It has been already shown that many fundamental physical laws may be derived using EPI. In this paper, the EPI approach is applied to the restoration problem, wherein it regards the unknown restoration as another fundamental law. It models the source information J as obeying Poisson statistics, and assumes additional image distortions that are due to additive Gaussian noise and quantization of the image data. It is found that the quantization level determines the degree of smoothness (or sharpness) of the restored signal. An optimal level of image quantization can be accomplished by adjusting its cross entropy. Finally, the restoration method by EPI is validated by numerical simulations of the image forming and restoring system.