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Digital signal processing solutions to 2-D finite support blind deconvolution problems

The 2-D discrete blind deconvolution problem is to reconstruct an image defined at integer coordinates and having known finite spatial extent from its 2-D convolution with a similar and also-unknown point-spread function. This is significantly more difficult than the typical image restoration problem of deconvolving a known blurring function. Many methods for solving this problem are iterative and alternate between the spatial and wavenumber domains. These algorithms are not POCS and they tend to stagnate. We present a completely novel approach that uses a battery of digital signal processing algorithms to produce an algorithm that comes close to expressing the solution in closed form. The only requirement on the image and point-spread functions are that they each have finite spatial extent and be roughly bandlimited, so that a fractional spatial shift also has finite spatial extent (this requirement is almost always met in practice).