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Journal Articles Signal Processing Year : 2023

Space-Variant Image Reconstruction via Cauchy Regularisation: Application to Optical Coherence Tomography

Abstract

We propose an adaptive, smooth, non-convex and sparsity-promoting variational model for singleimage super-resolution of real murine Optical Coherence Tomography (OCT) data. We follow a sparse-representation approach where sparsity is modelled with respect to a suitable dictionary generated from high-resolution OCT data. To do so, we employ pre-learned dictionaries tailored to model α-stable statistics in the non-Gaussian case, i.e. α < 2. The image reconstruction problem renders here particularly challenging due to the high level of noise degradation and to the heterogeneity of the data at hand. As a regulariser, we employ a smooth, non-convex and separable Cauchy-type penalty. To favour adaptivity to heterogeneous image contents, we propose a space-variant modelling by which the local degree of non-convexity encoded patch-wise within the local Cauchy shape parameter is estimated via maximum likelihood. For the solution of the patch-based smooth non-convex optimisation problems, we consider an extension of the cautious Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm where the descent direction is suitably updated depending on the local convexity behaviour of the functional. Our numerical results show that the combination of a space-variant modelling with a fast optimisation strategy improves reconstruction results, maintaining tissue texture and suppressing background noise to a desirable amount at the same time. Furthermore, the proposed optimisation strategy significantly reduces the computational efforts which often represent a major limitation in the analysis of OCT data.
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Dates and versions

hal-03594202 , version 1 (02-03-2022)
hal-03594202 , version 2 (21-12-2022)

Identifiers

Cite

Alin Achim, Luca Calatroni, Serena Morigi, Gabriele Scrivanti. Space-Variant Image Reconstruction via Cauchy Regularisation: Application to Optical Coherence Tomography. Signal Processing, 2023, 205, ⟨10.1016/j.sigpro.2022.108866⟩. ⟨hal-03594202v2⟩
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