Inverse Radon transforms: analytical and Tikhonov-like regularizations of inversion

TL;DR

This paper introduces an enhanced Tikhonov regularization method for inverse Radon transforms, incorporating an analytical term to improve the accuracy and robustness of physical quantity reconstructions.

Contribution

It proposes a new analytical term in Tikhonov regularization, extending the inversion framework and improving reconstruction quality in inverse Radon transform applications.

Findings

New optimization conditions derived for regularization

Enhanced robustness and accuracy demonstrated

Applicable to diverse physical inverse problems

Abstract

We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new analytical term to the Tikhonov regularization of Moore-Penrose's inversion procedure, we derive new optimization conditions that extend the Tikhonov regularization framework and influence the fitting parameter. This enhancement yields a more robust and accurate reconstruction of physical quantities, demonstrating its potential impact on various studies. We illustrate the significance of new term through schematic examples of physical applications, highlighting its relevance to diverse fields. Our findings provide a valuable tool for improving inversion methods and their applications in physics and beyond.