MATHEMATICAL RECONSTRUCTION OF SIGNALS AND IMAGES USING TEST TRIALS: A NON-BLIND APPROACH

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Abstract

The paper considers a mathematical method for the non-blind recovery of regular and multidimensional signals, including images distorted in processing by linear stationary systems. Instead of transfer functions, which are often difficult to determine, this method directly utilizes the trial test signals of processing systems to non-blindly recover of the signal from the test equation. The use of test signals belonging to the class of core functions greatly simplifies the signal recovery procedure and makes it more accurate and robust. The operator approach based on the multivariate convolution equation significantly improves the speed of numerical computation. Regularization technique is used to solve incorrectly posed and ill-conditioned problems, which allows efficiently recovering of real nondeterministic signals with noise and uncertainties. The influence of the test signals type on the recovery accuracy is analyzed and a method of their formation is proposed in the paper. Numerical experiments demonstrating the stability and efficiency of the proposed algorithm when recovering one-dimensional signals and two-dimensional images at high level of noise and uncertainties in data are considered. The proposed technique is able to improve the quality of signal and image processing without the need to modify complex and expensive equipment, to expand the field of practical application of mathematical reconstruction methods. Program codes and datasets are available at: https://github.com/novikov-borodin/data-rec.

About the authors

A. V. Novikov-Borodin

Institute for Nuclear Research (INR), Russian Academy of Sciences

Email: novikov.borodin@gmail.com
Moscow, Russia

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