Estimating Sparse Signals with Smooth Support via Convex Programming and Block Sparsity
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Date
2016
Publication Type
Conference Paper
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no
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OPEN ACCESS
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Abstract
Conventional algorithms for sparse signal recovery and sparse representation rely on l1-norm regularized variational methods. However, when applied to the reconstruction of sparse images, i.e., images where only a few pixels are non-zero, simple l1-norm-based methods ignore potential correlations in the support between adjacent pixels. In a number of applications, one is interested in images that are not only sparse, but also have a support with smooth (or contiguous) boundaries. Existing algorithms that take into account such a support structure mostly rely on nonconvex methods and-as a consequence-do not scale well to high-dimensional problems and/or do not converge to global optima. In this paper, we explore the use of new block l1-norm regularizers, which enforce image sparsity while simultaneously promoting smooth support structure. By exploiting the convexity of our regularizers, we develop new computationally-efficient recovery algorithms that guarantee global optimality. We demonstrate the efficacy of our regularizers on a variety of imaging tasks including compressive image recovery, image restoration, and robust PCA.
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published
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Book title
Proceedings of the 29th IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2016)
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Pages / Article No.
5906 - 5915
Publisher
IEEE
Event
29th IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2016)
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09695 - Studer, Christoph / Studer, Christoph