ИСТИНА

The reconstruction of an image distorted by a linear transformation is a problem unstable with respect to the perturbation of the mathematical model of the formation of this image. This instability is overcome by using a priori information about the class of original images. One of the ways to attract such information is the assumption that the original image belongs to the class of piecewise constants. The class of piecewise constant functions is a good approximating class for signals encountered in practice, since such functions can be arbitrarily accurately approximate any (square integrable) signal. On the other hand, in a number of applied studies, the assumption that the brightness value of the image takes a finite number of values is plausible. Such a proposal, in particular, is made in the tomography of objects, when the studied sample consists of a small number of fractions. In this paper, we propose an algorithm for reconstructing a piecewise constant signal blurred by a linear transformation, and investigate the possibility of its application to estimate the original unblurred signal. For ease of implementation, the case of one-dimensional signals is considered.