A comparison of regularization operators for noisy gamma-ray tomographic reconstruction

Abstract

The severe effects of several types of noise present in tomographic image reconstruction are well known. Some of these are a consequence of the ill-posedness of this inverse problem. In this work, we investigate the impact of a Tikhonov regularization on the solution of a gamma-ray tomography reconstruction by means of a least squares numerical method. The theoretical methodology is considered in a broad sense as a Tikhonov regularization, but also includes the Morozov concept used specifically for the delta parameter control. The reconstruction quality shows effective improvement when this technique is applied to simple gamma-ray tomography algorithms. Furthermore, the impact of these regularization techniques on the solutions of linear systems of equations is significant. An ART (Algebraic Reconstruction Technique)-type algorithm was used for the reconstruction of simulated data utilizing built-in Matlab functions. These were compared with data obtained through a regularization implemented with TSVD (Truncated Singular Value Decomposition), as well as data obtained through hybrid algorithms such as TSVD plus Toepelitz, tridiagonal and identity operators. The quality of the resulting reconstruction is evaluated through RMSE (Root Mean Square Error). Direct comparisons suggest that for a high noise level and high delta parameter the TSVD plus tridiagonal operator is the best choice.