Versatile and Scalable Cosparse Methods for Physics-Driven Inverse Problems

Kitić, Srđan; Bensaid, Siouar; Albera, Laurent; Bertin, Nancy; Gribonval, Rémi

doi:10.1007/978-3-319-69802-1_10

Cited by 2 publications

(1 citation statement)

References 71 publications

(131 reference statements)

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“…These can however not be fairly compared to our method. The method the authors of [17,18] mainly advertise uses a different type of sparsity than we do. In their setting, Au is sparse in a certain sense, where A is an analysis operator.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Compressed Sensing: From Theory to Praxis

Flinth¹,

Hashemi²,

Kutyniok³

2017

Compressive Sensing of Earth Observations

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We propose a scheme utilizing ideas from infinite dimensional compressed sensing for thermal source localization. Using the soft recovery framework of one of the authors, we provide rigorous theoretical guarantees for the recovery performance. In particular, we extend the framework in order to also include noisy measurements. Further, we conduct numerical experiments, showing that our proposed method has strong performance, in a wide range of settings. These include scenarios with few sensors, off-grid source positioning and high noise levels, both in one and two dimensions.objective function based on the Unit-Norm-Tight-Frame (UNTF) concept. Although the paper emphasizes on empirical aspects, theoretical claims are also derived.Excluding [23,22], all of the previously mentioned works do not explicitly try to utilize the useful structures which exist for diffusion sources, such as sparsity and spatiotemporal correlation among measurement governed by a PDE constraint. In particular, none of them use the powerful framework of compressed sensing [2]. Therefore, Rostami et al. [34] proposed a compressed sensing method for reconstructing the diffusion field by incorporating PDE constraints in recovery part as a side information. This effort was extended to the 2D scenario in [15] by one of the authors of this article, together with co-authors. In a similar way but by utilizing an analysis formulation for the source localization problem, [17] consider the source localization inverse problem for other types of sources or governing equations, with PDE side information in a co-sparse framework.

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Section: Numerical Experimentsmentioning

confidence: 99%