Direct Reconstruction of Distorted Signals and Images Using Shifts Methods

Abstract

Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind deconvolution without using approximations and integral transforms. Methods are fast and effective for accurate data reconstruction, which gives a possibility of increasing the effective resolution of measuring systems by mathematical methods up to physical limits without solving the expensive and quite difficult scientific and technical problems. Step-by-step and combined shifts methods supplement each other in data reconstruction at different distortions of signals, noise levels and data volumes. Methods may be adapted for reconstruction of multi-dimensional data. There are considered the restorations of 2D images blurred by uniform motion and distorted by functions, which may be factored, such as Gaussian-like functions. The comparative analysis of step-by-step and combined shifts methods is presented. Reconstruction inaccuracies are estimated. Examples of signal reconstructions and image restorations at different distortions are considered.

Submitted to IEEE Trans on Signal Processing, 14-Jan-2019