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.
Highlights
X-ray computed tomography (XCT) is an important diagnostic tool used in medicine
This paper studies the problem of efficiently tuning the hyper-parameters in penalised least-squares reconstruction for XCT
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
Summary
X-ray computed tomography (XCT) is an important diagnostic tool used in medicine. Recently, with the improvement of resolution and increase of energy, the technology is increasingly used for industrial application. The problem of image reconstruction in XCT considered in the present paper belongs to the wider family of inverse problems of the type: given a set of projections, concatenated into a vector y ∈ Y , and a forward operator A: X 7→ Y , find x s.t. kA( x ) − yk2 ≤ e. Recent advances in the field of MRI reconstruction opened the door to a whole new family of regularisations, based on the discovery that, in an appropriate dictionary, some features of the sought vector x are sparse. This breakthrough discovery appeared essential in the field of Compressed. On of the latest development in this area is the design of Total Variation type of regularisation functionals [6] and associated fast reconstruction algorithms [7,8]
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