Article
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Application of the Model of Spots for Inverse Problems
Version 1
: Received: 21 December 2022 / Approved: 22 December 2022 / Online: 22 December 2022 (07:14:16 CET)
A peer-reviewed article of this Preprint also exists.
Simonov, N.A. Application of the Model of Spots for Inverse Problems. Sensors 2023, 23, 1247. Simonov, N.A. Application of the Model of Spots for Inverse Problems. Sensors 2023, 23, 1247.
Abstract
This article proposes application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using the deep learning. In general, the spots represent vague figures in abstract “information spaces” or crisp figures with lack of in-formation about their shapes and are adequate for representation human mental images and reasoning in Artificial Intelligence (AI). However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, basing on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Also, we defined L4 vectors, L4 matrices, and mathematical operations on them. Developed apparatus can be used in AI, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates application of spot-based inverse Radon algorithm for binary image reconstruction.
Keywords
inverse problems; image reconstruction; vague figures; mental images; Artificial Intelligence
Subject
Computer Science and Mathematics, Information Systems
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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