Superresolving image restoration using linear programming

Superresolving image restoration (SIR) in the presence of noise is considered. Few SIR algorithms havedemonstrated the ability to resolve two point sources spaced one-half of the Rayleigh distance apart. In thispaper, it is shown that the SIR of a two-point noncoherent source spaced one-tenth of a Rayleigh distanceapart 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 fittingis used. It is also shown that for a diffraction-limited image of two-point sources spaced one-half of the Rayleighdistance apart, where the input is contaminated with significant noise, SIR is achievable. These resultshave important implications in atmospheric physics, geophysics, radio astronomy, medical diagnostics, and digital bandwidth-compression applications where the deconvolution of noisy bandwidth-compressedimages is one of the fundamental limitations. The techniques described are specifically designed for impulsive-type images.