Invariants to Convolution in Arbitrary Dimensions

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Processing of multidimensional image data which were acquired by a linear imaging system of unknown point-spread function (PSF) is an important problem whose solution usually requires image restoration based on blind deconvolution (BD). Since BD is an ill-posed and often impossible task, we propose an alternative approach that enables to skip the restoration. We introduce a new class of image descriptors which are invariant to convolution of the original image with arbitrary centrosymmetric PSF. The invariants are based on image moments and can be defined in the spectral domain as well as in the spatial domain. The paper presents theoretical results as well as numerical examples and practical applications.

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