Using Test Trials of Processing Systems for Non-Blind Recovery of Signals and Images

The mathematical method for non-blind recovery of one-dimensional and multidimensional signals, including images, distorted during processing by linear stationary (or time-invariant) systems is considered. Instead of transfer functions, which are often difficult to determine because they belong to the class of generalized functions, the proposed method uses test trial signals of processing systems for signal recovery. Unlike the transfer functions, the test signals belong to the class of ordinary functions, which simplifies the signal reconstruction procedure considerably and makes it more accurate and stable. It also allows existing methods, such as regularization technique, to be effectively used to solve ill-posed and ill-conditioned problems for recovering nondeterministic signals with high levels of noise and uncertainty. The proposed operator approach based on the multidimensional convolution equation significantly reduces the number of operations and increases the speed of numerical computations. The considered method allows improving the quality of signal and image processing without complex and expensive modernization of the equipment. Received: 9 December 2024 | Revised: 7 March 2025 | Accepted: 10 September 2025 Conflicts of Interest The author declares that he has no conflicts of interest to this work. Data Availability Statement The data that support the findings of this study are openly available in GitHub at https://github.com/novikov-borodin/data-rec. Author Contribution Statement Andrey V. Novikov-Borodin: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Project administration, Funding acquisition.