Abstract
Deconvolution of images of the same object from multiple sensors with different point spread functions (PSF), as shown by Berenstein and Patrick, can be a well-posed problem in the sense of distributions if the PSF satisfy some suitable conditions. More precisely, if these operators are represented by compactly supported distributions, a corresponding set of deconvolvers, also given by compactly supported distributions, may exist. Nevertheless, it must be observed that this inverse operator is not particularly useful if the multiple images which must be deconvolved are affected by noise, because continuity in the sense of distributions is too weak. This is the reason why a more effective approach is provided by the inverse methods typical of regularization theory. We have considered the case described by Berenstein and Patrick, in which the input function consists of the sum of two Gaussian pulses and the PSF are the characteristic functions of the intervals (-1, 1) and (- (root)2, 2). The two images we have obtained have been affected by Gaussian noise and then simulated data have been inverted by using various regularization techniques; in particular, in the case of iterative methods, it has also been possible to introduce the positivity constraint. The comparison between the reconstructions we have obtained and the input function allows to estimate the greater efficiency of the regularized multiple operators deconvolution, compared with the inversion of a single image, when linear filtering is applied. On the contrary the performance of the nonlinear constrained iterative method seems not to be particularly sensitive to the use of two images instead of one. An explanation of this fact is given and an example, where the use of multiple images can be advantageous, is presented.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Michele Piana, Mario Bertero, "Deconvolution of multiple images", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224169; https://doi.org/10.1117/12.224169
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