# Direct Reconstruction of Distorted Signals and Images Using Shifts Methods

## TL;DR

This paper introduces direct, non-blind deconvolution methods using shifts for reconstructing distorted signals and images, enhancing resolution without complex approximations or transforms.

## Contribution

It proposes novel shift-based deconvolution techniques that improve data reconstruction accuracy and efficiency, applicable to multi-dimensional data and various distortion types.

## Key findings

- Methods are fast and effective for accurate data reconstruction.
- Applicable to 2D images blurred by motion and Gaussian-like distortions.
- Comparative analysis shows their effectiveness across different noise levels.

## 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.

---
Source: https://tomesphere.com/paper/1901.07953