Correction, Reconstruction, and Modeling of Experimental Data Using LI Transforms

Abstract

This paper examines mathematical methods of using the linear invariant (LI) transforms for the correction, reconstruction, and modeling of experimental data—one-dimensional and multidimensional signals including images distorted during processing by LI systems, which in the 1D case are the linear stationary or time-invariant systems. Methods enable data processing with a minimum of initial information and computational resources; they are simple, require minimal resources for numerical calculations, and can be effectively used to process data of large volumes. LI methods have virtually no restrictions on the class of processing functions, which must be locally integrable in the domain under consideration. LI methods are effective and designed to solve some typical signal processing problems often encountered in practice. This paper provides examples of the practical application of LI methods for signal processing of electronic devices, time-of-flight neutron spectrometers, image processing, etc. Mathematical LI methods can improve the quality of data processing and enhance the effective parameters of processing systems without solving complex scientific, technical, and technological problems or creating expensive equipment.

Received: 27 November 2025 | Revised: 16 April 2026 | Accepted: 22 May 2026

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

The program codes used in this study are publicly available in the author's domain of the GitHub library at https://github.com/novikov-borodin/lst-data-proc. These codes can be used for free, but references to the author's work and the author's code domain are required.

Author Contribution Statement

Andrey Novikov-Borodin: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration, Funding acquisition.