Superresolving image restoration using linear programming

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Abstract
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.

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