Restoration of Binary Images Using Positive Semidefinite Programming

We present a novel approach, using positive semidefinite (PSD) programming, to restore blurred and noisy binary images when the point spread function (PSF) is known. The combinatorial nature of the problem is noted: binary image deconvolution requires the minimization of an energy function over binary variables, taking into account not only local similarity and spatial context, but also the relationship between individual pixel values and the PSF. Due to the high computational load the deconvolution process of a large image might face, we segment the binary image into smaller blocks before deconvolving each block. To suppress error propagation, we also process image blocks with different overlapping lines and columns. Superiority of the proposed PSD binary image restoration approach is confirmed by numerical experiments