An Algebraic Solution for Discrete Tomography

Yagle, A.E.

doi:10.1007/978-1-4612-1568-4_11

Cited by 1 publication

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“…The algebraic methods exploit the algebraic structure of the problem and may give some insight into the (non-) uniqueness and the required number of projections [13], [14]. While theoretically very elegant, these methods are not readily generalised to realistic projection models and noisy data.…”

Section: B Literature Reviewmentioning

confidence: 99%

A Convex Formulation for Binary Tomography

Kadu

Leeuwen

2020

IEEE Trans. Comput. Imaging

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Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a constrained least-squares problem. As the constraints are non-convex, many approaches for solving it rely on either relaxing the constraints or heuristics. In this paper we propose a novel convex formulation, based on the Lagrange dual of the constrained least-squares problem. The resulting problem is a generalized LASSO problem which can be solved efficiently. It is a relaxation in the sense that it can only be guaranteed to give a feasible solution; not necessarily the optimal one. In exhaustive experiments on small images (2×2, 3 × 3, 4 × 4) we find, however, that if the problem has a unique solution, our dual approach finds it. In case of multiple solutions, our approach finds the commonalities between the solutions. Further experiments on realistic numerical phantoms and an experiment on X-ray dataset show that our method compares favourably to Total Variation and DART.

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Section: B Literature Reviewmentioning

confidence: 99%