Superresolving image restoration using linear programming

Superresolving image restoration (SIR) in the presence of noise is considered. Few SIR algorithms have demonstrated the ability to resolve two point sources spaced one-half of the Rayleigh distance apart. In this paper, it is shown that the SIR of a two-point noncoherent source spaced one-tenth of a Rayleigh distance apart is possible. The method presented uses optimal data fitting techniques based on the methods of linear programming. For noisy images, a combination of linear eigenvalue prefiltering and optimal data fitting is used. It is also shown that for a diffraction-limited image of two-point sources spaced one-half of the Rayleigh distance apart, where the input is contaminated with significant noise, SIR is achievable. These results have important implications in atmospheric physics, geophysics, radio astronomy, medical diagnostics, and digital bandwidth-compression applications where the deconvolution of noisy bandwidth-compressed images is one of the fundamental limitations. The techniques described are specifically designed for impulsive-type images.

Digital image restoration using quadratic programming

The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given.

New methods for picture reconstruction: recursive and causal techniques

The methods proposed by Kashyap and Mittal [1], [2] for the reconstruction of pictures from projections are reformulated under a regression model. These reinterpretations are based on least-squares and Bayesian formulations of a statistical linear model and lead to the derivation of recursive and causal algorithms which are more efficient. Experimental results with simulation of the filters are also presented.