The algorithm for reconstruction piecewise constant image distorted by a linear transformation

N. G. Mikheev; A. I. Chulichkov; V. A. Antonyuk

doi:10.1117/12.2557046

31 January 2020 The algorithm for reconstruction piecewise constant image distorted by a linear transformation

N. G. Mikheev, A. I. Chulichkov, V. A. Antonyuk

Proceedings Volume 11433, Twelfth International Conference on Machine Vision (ICMV 2019); 114331S (2020) https://doi.org/10.1117/12.2557046
Event: Twelfth International Conference on Machine Vision, 2019, Amsterdam, Netherlands

Abstract

The reconstruction of an image distorted by a linear transformation is a problem that is unstable with respect to the perturbation of the mathematical model of the image formation. This instability is overcome by using a priori information about the class of original images. Among the ways to use such information, there is an assumption that the original image belongs to the class of piecewise constant images. The class of piecewise constant functions can provide a good approximation for signals encountered in practice since such functions can approximate any square-integrable signal with arbitrary accuracy. On the other hand, the assumption that the brightness value of the image takes a finite set of values is plausible for some applied studies. Such a proposal, in particular, is made in the tomography, where studied samples can consist of a small number of fractions. In this paper, we propose an algorithm for reconstruction of piecewise constant signals blurred by a linear transformation and investigate the possibility of its application to the original unblurred signal estimation. For ease of implementation, the case of one-dimensional signals is considered.

Citation Download Citation

N. G. Mikheev, A. I. Chulichkov, and V. A. Antonyuk "The algorithm for reconstruction piecewise constant image distorted by a linear transformation", Proc. SPIE 11433, Twelfth International Conference on Machine Vision (ICMV 2019), 114331S (31 January 2020); https://doi.org/10.1117/12.2557046

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