| Methods for the restoration of images corrupted by blur and noise are presented. During transmission through an optical or electrical channel, images become corrupted by blur and noise as a result of channel limitations (i.e. optical aberrations or a bandlimit). If images are treated as a matrix whose elements (pixels) assume a finite number of values then there is a large but finite set of possible images that can be transmitted. By treating this finite set as a ‘signal’ set, digital communications methods may be used to estimate the uncorrupted image given a blurred and noisy version. Specifically, row-by-row estimation, decision-feedback and vector-quantization are used to extend the 1D sequence estimation ability of the a-posteriori probability (APP) and Viterbi algorithm (VA) to the estimation of 2D images. Simulations show the 2D VA and APP algorithms return near-optimal estimates of binary images as well as improved estimates of greyscale images when compared with the conventional Wiener filter (WF) estimates. Unlike the WF, the VA and APP algorithms are shown to be capable of super-resolution and adaptable for use with signal-dependent Poisson noise corruption. Restorations of experimental data gathered from an optical imaging system are presented to support simulation results. |
