Manifold sparse beamforming

Gözcü, Baran; Asaei, Afsaneh; Cevher, Volkan

doi:10.1109/camsap.2013.6714020

2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) 2013

DOI: 10.1109/camsap.2013.6714020

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Manifold sparse beamforming

Baran Gözcü¹,

Afsaneh Asaei²,

Volkan Cevher³

Abstract: Abstract-We consider the minimum variance distortionless response (MVDR) beamforming problems where the array covariance matrix is rank deficient. The conventional approach handles such rank-deficiencies via diagonal loading on the covariance matrix. In this setting, we show that the array weights for optimal signal estimation can admit a sparse representation on the array manifold. To exploit this structure, we propose a convex regularizer in a grid-free fashion, which requires semi-definite programming. We t… Show more

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2014

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Convexity in Source Separation : Models, geometry, and algorithms

McCoy

Cevher

Dinh

et al. 2014

IEEE Signal Process. Mag.

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Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems.Recent advances in convex optimization provide a simple framework for efficiently solving numerous difficult demixing problems. This article provides an overview of the emerging field, explains the theory that governs the underlying procedures, and surveys algorithms that solve them efficiently. We aim to equip practitioners with a toolkit for constructing their own demixing algorithms that work, as well as concrete intuition for why they work. Fundamentals of demixingThe most basic model for mixed signals is a superposition model, where we observe a mixed signal z 0 ∈ R d of the formand we wish to determine the component signals x 0 and y 0 . This simple model appears in many guises. Sometimes, superimposed signals come from basic laws of nature. The amplitudes of electromagnetic waves, for example, sum together at a receiver, making the superposition model (1) common in wireless communications. Similarly, the additivity of sound waves makes superposition models natural in speech and audio processing.Other times, a superposition provides a useful, if not literally true, model for more complicated nonlinear phenomena. Images, for example, can be modeled as the sum of constituent featuresthink of stars and galaxies that sum to create an image of a piece of the night sky [1]. In machine learning, superpositions can describe hidden structure [2], while in statistics, superpositions can model gross corruptions to data [3]. These models also appear in texture repair [4], graph clustering [5], and line-spectral estimation [6].A conceptual understanding of demixing in all of these applications rests on two key ideas. Low-dimensional structures: Natural signals in high dimensions often cluster around lowdimensional structures with few degrees of freedom relative to the ambient dimension [7].Examples include bandlimited signals, array observations from seismic sources, and natural

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Convexity in Source Separation : Models, geometry, and algorithms

McCoy

Cevher

Dinh

et al. 2014

IEEE Signal Process. Mag.

Self Cite

View full text Add to dashboard Cite

show abstract

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Manifold sparse beamforming

Cited by 1 publication

References 8 publications

Convexity in Source Separation : Models, geometry, and algorithms

Convexity in Source Separation : Models, geometry, and algorithms

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