Efficient Hyper-Parameter Selection in Total Variation-Penalised XCT Reconstruction Using Freund and Shapire’s Hedge Approach

Abstract

This paper studies the problem of efficiently tuning the hyper-parameters in penalised least-squares reconstruction for XCT. Discovered through the lens of the Compressed Sensing paradigm, penalisation functionals such as Total Variation types of norms, form an essential tool for enforcing structure in inverse problems, a key feature in the case where the number of projections is small as compared to the size of the object to recover. In this paper, we propose a novel hyper-parameter selection approach for total variation (TV)-based reconstruction algorithms, based on a boosting type machine learning procedure initially proposed by Freund and Shapire and called Hedge. The proposed approach is able to select a set of hyper-parameters producing better reconstruction than the traditional Cross-Validation approach, with reduced computational effort. Traditional reconstruction methods based on penalisation can be made more efficient using boosting type methods from machine learning.