Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes extita priori knowledge regarding features of typical images such as smoothness or sharpness. This maximization can be performed with standard local optimization tools when the function is concave, but it is generally intractable for realistic priors, which are non-concave. We introduce a new method to reconstruct images obtained from Radon projections by using Expectation Propagation, which allows us to reframe the problem from an Bayesian inference perspective. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, Expectation Propagation paired with very simple but non log-concave priors, is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.

Non-convex image reconstruction via expectation propagation / Paola Muntoni, Anna; DIAZ HERNANDEZ ROJAS, RAFAEL ALBERTO; Braunstein, Alfredo; PAGNANI, Andrea; PEREZ CASTILLO, Isaac. - In: PHYSICAL REVIEW. E. - ISSN 2470-0053. - 100:23(2018). [10.1103/PhysRevE.100.032134]

Non-convex image reconstruction via expectation propagation

Rafael Díaz Hernández Rojas
Secondo
;
Andrea Pagnani;Isaac Pérez Castillo
2018

Abstract

Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes extita priori knowledge regarding features of typical images such as smoothness or sharpness. This maximization can be performed with standard local optimization tools when the function is concave, but it is generally intractable for realistic priors, which are non-concave. We introduce a new method to reconstruct images obtained from Radon projections by using Expectation Propagation, which allows us to reframe the problem from an Bayesian inference perspective. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, Expectation Propagation paired with very simple but non log-concave priors, is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.
2018
image reconstruction; non-convex problems; Bayesian methods; expectation propagation
01 Pubblicazione su rivista::01a Articolo in rivista
Non-convex image reconstruction via expectation propagation / Paola Muntoni, Anna; DIAZ HERNANDEZ ROJAS, RAFAEL ALBERTO; Braunstein, Alfredo; PAGNANI, Andrea; PEREZ CASTILLO, Isaac. - In: PHYSICAL REVIEW. E. - ISSN 2470-0053. - 100:23(2018). [10.1103/PhysRevE.100.032134]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1279675
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