Generalized Versus Classical Maximum Entropy for Imaging

Abstract

The problem of image reconstruction from incomplete and noisy complex Fourier spectrum is considered. The maximum entropy method (MEM) is of great interest as the most effective nonlinear reconstruction method having superresolution effect. Because objects of radio astronomical observations are incoherent radio sources described by real non-negative distributions, application of the classical MEM is quite reasonable. But it is established that the MEM gives acceptable reconstruction quality mostly in the case of point-like sources and in general it does not ensure satisfactory reconstruction of continous, graytone objects, which can considerably restrict applications of the MEM in astronomy. The generalized maximum entropy method (GMEM) was originally proposed for reconstruction of distributions described by complex functions (Bajkova, 1992) and was considered as having the same properties of the classical MEM. More careful analysis of the GMEM and classical MEM for real non-negative objects allowed to establish that the GMEM ensures much more exact reconstruction, especially in the case of continous objects. Explanation and demonstration of this interesting and very important phenomenon is the purpose of the present paper.