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Sparse Recovery and Dictionary Learning From Nonlinear Compressive Measurements

Rencker, Lucas, Bach, Francis, Wang, Wenwu and Plumbley, Mark D. (2019) Sparse Recovery and Dictionary Learning From Nonlinear Compressive Measurements IEEE TRANSACTIONS ON SIGNAL PROCESSING, 67 (21). pp. 5659-5670.

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Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements. These problems have often been addressed by solving constrained sparse coding problems, which can be difficult to solve, and assuming that the sparsifying dictionary is known and fixed. Here we propose a simple and unified framework to deal with nonlinear measurements. We propose a cost function that minimizes the distance to a convex feasibility set, which models our knowledge about the nonlinear measurement. This provides an unconstrained, convex, and differentiable cost function that is simple to optimize, and generalizes the linear least squares cost commonly used in sparse coding. We then propose proximal based sparse coding and dictionary learning algorithms, that are able to learn directly from nonlinearly corrupted signals. We show how the proposed framework and algorithms can be applied to clipped, quantized and 1-bit data.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering > Centre for Vision Speech and Signal Processing
Authors :
Bach, Francis
Plumbley, Mark
Date : 1 November 2019
Funders : European Union H2020 Framework Programme (H2020-MSCA-ITN-2014)
DOI : 10.1109/TSP.2019.2941070
Copyright Disclaimer : © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Uncontrolled Keywords : Sparse coding; Dictionary learning; Nonlinear measurements; Saturation; Quantization; 1-bit sensing
Depositing User : Diane Maxfield
Date Deposited : 24 Oct 2019 09:12
Last Modified : 24 Oct 2019 09:12

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