9 October 1995 Numerical fovea: an efficient solution to discrete inverse problems
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Abstract
Traditional successful approaches to inverse problem solutions usually deal with continuous variable domains: image inversion is a key example of such a problem. In the present paper the mathematical base for a novel efficient algorithm for inversion problems is discussed. The proposed procedure, called the numerical Fovea, is a general discrete algorithm tuned to image inversion problems and matches the basic characteristics of the human visual system. In fact distance, working in feedback. This kind of structure allows for the formation of images according to the binocular field of view. The represented algorithm operates in a discrete variable domain. Beyond the advantages in terms of simplicity and computational speed, it agrees with the results of biological observation which reveal that the elements sensitive to light stimuli are finite in number. Thus, the domain of interest can be modeled as a couple of bi-dimensional lattices having the mathematical structure of discrete vector groups, consistently with the geometrical receptor displacement in the human fovea. The receptor multilayer structure can be described by a recursive relation. A numerical example is presented: for every source reconstruction problem an optimal computational precision level can be selected according to the required accuracy.
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Gianfranco F. Dacquino, Rodolfo A. Fiorini, B. Cattaneo, A. Fabiani, "Numerical fovea: an efficient solution to discrete inverse problems", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224180; https://doi.org/10.1117/12.224180
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