Review of Interstripation Methods in the Lagrange Form for Approximating Continuous Functions of Two Variables

The article presents a review of modern approaches to the construction and study of new information operators. For functions, information about which is known only on a certain system of strips, examples of information operators of interstripation are given for approximating the values of continuous functions of two variables. This work is devoted to information operators of polynomial interstripation in the Lagrange form for approximating the values of two-dimensional continuous functions, information about which is known on a certain system of strips of a special form. Such problems often arise when processing data from remote sensing of the planet, aerial reconnaissance, etc. This paper presents the basic concepts of the trace of a function on a strip, the trace of a function on a line. Based on these definitions, interstripation operators are given for strips, the boundaries of which are parallel to the coordinate axes. The polynomial Lagrange interstripation operators for approximating values between non-intersecting strips whose boundaries are parallel to each other and parallel to the Ox axis, the polynomial Lagrange interstripation operators for approximating values between non-intersecting strips whose boundaries are parallel to the Oy axis, and the polynomial Lagrange interstripation operators for approximating values between intersecting strips whose boundaries are parallel to the coordinate axes are considered. A series of computational experiments were conducted to restore the values of the function between different systems of strips proposed by the interstripation operators in the Lagrange form. Information operators are used in various fields of science and technology. Interstripation operators can be used in processing data of remote sensing of the planet, aerial reconnaissance, radar location by side-scan radars, etc. In addition, in further research related to information interstripation operators, a promising direction is their application in various image processing algorithms.