Experimental Data Processing Using Shift Methods

Andrey Novikov-Borodin,Gh Adam,J Buša,M Hnatič

doi:10.1051/epjconf/202022603014

Abstract

The numerical methods of step-by-step and combined shifts are proposed for correction and reconstruction the experimental data convolved with different blur kernels. Methods use a shift technique for the direct deconvolution of experimental data, they are fast and effective for data reconstruction, especially, in the case of discrete measurements. The comparative analysis of proposed methods is presented, inaccuracies of reconstruction with different blur kernels, different volumes of data and noise levels are estimated. There are presented the examples of using the shift methods in processing the statistical data of TOF neutron spectrometers and in planning the proton therapy treatment. The multi-dimensional data processing using shift methods is considered. The examples of renewal the 2D images blurred by uniform motion and distorted with the Gaussian-like blur kernels are presented.

Highlights

A convolution is a widespread transformation in experimental data
The proposed numerical methods of step-by-step and combined shifts have quite simple algorithms and in a number of cases are more effective for data reconstruction than the existing methods of the direct matrix inversion and the methods based on the integral transformations or the regularization technique [3, 4]
The numerical methods of step-by-step and combined shifts are proposed for the discrete data processing by means of a shift technique

Summary

Introduction

A convolution is a widespread transformation in experimental data. It already appears as a result of overlapping the hypothetical ideal momentary signals during the time of the measurements and looks like the signal distortion. A deconvolution is needed to reconstruct the momentary signals from the distorted data to increase the accuracy of the measurements. The possibility of data reconstruction depends on many factors and it makes the development of different reconstruction techniques an actual and challenging research topic. The proposed numerical methods of step-by-step and combined shifts have quite simple algorithms and in a number of cases are more effective for data reconstruction than the existing methods of the direct matrix inversion and the methods based on the integral transformations or the regularization technique [3, 4]

Algorithms of shift methods

Image renewal

Conclusion