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Erschienen in:
Introduction to Compressed Sensing and Sparse Filtering Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

4. Nuclear Norm Optimization and Its Application to Observation Model Specification

verfasst von : Ning Hao, Lior Horesh, Misha Kilmer

Erschienen in: Compressed Sensing & Sparse Filtering

Verlag: Springer Berlin Heidelberg

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Abstract

Optimization problems involving the minimization of the rank of a matrix subject to certain constraints are pervasive in a broad range of disciples, such as control theory [6, 26, 31, 62], signal processing [25], and machine learning [3, 77, 89]. However, solving such rank minimization problems is usually very difficult as they are NP-hard in general [65, 75]. The nuclear norm of a matrix, as the tightest convex surrogate of the matrix rank, has fueled much of the recent research and has proved to be a powerful tool in many areas. In this chapter, we aim to provide a brief review of some of the state-of-the-art in nuclear norm optimization algorithms as they relate to applications. We then propose a novel application of the nuclear norm to the linear model recovery problem, as well as a viable algorithm for solution of the recovery problem. Preliminary numerical results presented here motivates further investigation of the proposed idea.

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Vorheriges Kapitel Sparse Signal Recovery with Exponential-Family Noise
Nächstes Kapitel Nonnegative Tensor Decomposition
Fußnoten
1
This assumption is not mandatory for primal-dual interior point methods.
 
2
Non-intrusive methods relies upon black-box interface, for which output is received per input.
 
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Metadaten
Titel
Nuclear Norm Optimization and Its Application to Observation Model Specification
verfasst von
Ning Hao
Lior Horesh
Misha Kilmer
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
Buch
Compressed Sensing & Sparse Filtering

Print ISBN: 978-3-642-38397-7

Electronic ISBN: 978-3-642-38398-4

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-642-38398-4_4

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