Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Theory and Design of Soundfield Reproduction Using Continuous Loudspeaker Concept
IEEE Transactions on Audio, Speech, and Language Processing
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
Fast Solution of -Norm Minimization Problems When the Solution May Be Sparse
IEEE Transactions on Information Theory
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Reproducing a sampled sound field using an array of loudspeakers is a problem with well-appreciated applications to acoustics and ultrasound treatment. Loudspeaker signal design has traditionally relied on (possibly regularized) least-squares (LS) criteria. In many cases however, the desired sound field can be reproduced using only a few loudspeakers, which are sparsely distributed in space. To exploit this feature, the fresh look advocated here permeates benefits from advances in variable selection and compressive sampling to sound field synthesis by formulating a sparse linear regression problem that is solved using the least-absolute shrinkage and selection operator (Lasso). An efficient implementation of the Lasso for the problem at hand is developed based on a coordinate descent iteration. Analysis and simulations demonstrate that Lasso-based sound field reproduction yields better performance than LS especially at high frequencies and for reproduction of under-sampled sound fields. In addition, Lasso-based synthesis enables judicious placement of loudspeaker arrays.