Mathematical Restoration of Signals and Images Using Test Trials: A Non-Blind Approach

A mathematical method for non-blind restoration of one-dimensional and multidimensional signals including images distorted during processing by linear stationary systems is proposed. Instead of transfer functions, which are often difficult to determine, this method directly uses trial test signals of processing systems for non-blind restoration of a signal based on the test trial equation. The use of test signals belonging to the class of ordinary functions significantly simplifies the signal restoration procedure and makes it more accurate and stable. The operator approach based on the multidimensional convolution equation significantly increases the speed of numerical calculations. To solve ill-posed and ill-conditioned problems, a regularization technique is used that allows for effective re-storation of real nondeterministic noisy and uncertain signals. The influence of the type of test si-gnals on the restoration accuracy is analyzed, and a technique for their formation is proposed. Numerical experiments are considered that demonstrate the stability and efficiency of the proposed algorithm in restoring one-dimensional signals and two-dimensional images with a high level of noise and uncertainty. The proposed method can improve the quality of signal and image processing without the need to modify complex and expensive equipment and expand the scope of practical application of ma-thematical restoration methods.1