Maximum Entropy Principle in Image Restoration

Many imaging systems are faced with the problem of estimating a true image from a degraded dataset. In such systems, the image degradation is translated into a convolution with a Point Spread Function (PSF) and addition of noise. Often, the image recovery by inverse filtering is not possible because the PSF matrix is ill-conditioned. Maximum Entropy (MaxEnt) is an alternative method, which uses the entropy concept for estimating the true image. This paper presents MaxEnt method, starting with the historical references of the entropy concept and finalizing with its application in image restoration and reconstruction. The statistical model of MaxEnt for images is discussed and the connection of MaxEnt with the Bayesian inference is explained. MaxEnt is evaluated by using a modified version of Cornwell algorithm. Two cases are considered: images degraded by various PSF kernels in presence of additive noise and images resulted from incomplete datasets. The tests show PSNR gains ranging from 1 to 7dB for the degraded images and images reconstructed at 25dB from datasets with up to 80% missing pixels.