Introduction to compressive sensing in acoustics

Abstract

Compressive sensing (CS) in acoustics has received significant attention in the last decade, and thus motivates this special issue. CS emerged from the signal processing and applied math community and has since generated compelling results in acoustics. This special issue primarily addresses the acoustics CS topics of compressive beamforming and holography. For a sound field observed on a sensor array, CS reconstructs the direction of arrival of multiple sources using a sparsity constraint. Similarly, in holography a sparsity constraint gives improved sound field reconstruction over conventional ℓ-regularization. Other topics in this issue include sparse array configurations (as co-arrays) and sparse sensing in acoustic communication.

Machine learning in acoustics: Theory and applications

“…The solution to (19) is also known as the LASSO, 37 and forms the cornerstone of the field of compressive sensing (CS). 38,39 Whereas in the estimate w obtained from (17) many of the coefficients are small, the estimate from (19) has only few non-zero coefficients. Sparsity is a desirable property in many applications, including array processing 39,40 and image processing.…”

“…38,39 Whereas in the estimate w obtained from (17) many of the coefficients are small, the estimate from (19) has only few non-zero coefficients. Sparsity is a desirable property in many applications, including array processing 39,40 and image processing. 23 We give an example of 1 (in CS) and 2 regularization in the estimation of DOAs on a line array, Fig.…”

“…The second step of EM, called the M-step, updates the parameters by maximizing the auxiliary function, θ new = arg max θ Q(θ, θ old ), with the responsibilities r km from the E-step (39). 12,57 The M-step estimates of π (using also K k=1 π k = 1), µ k , and Σ k are…”

Detection of Direction-Of-Arrival in Time Domain Using Compressive Time Delay Estimation with Single and Multiple Measurements

“…Recently, compressive sensing (CS) has been combined with beamforming [ 4 , 5 , 6 , 7 , 8 ] to solve an underdetermined linear system [ 9 , 10 ]. In the conventional compressive beamforming technique [ 6 , 7 ], is the array-captured measurement vector in the frequency domain and is identical to the data used in classical beamforming schemes; is an unknown vector to be solved by CS, whose entries correspond to the amplitudes of the arrival angles in predefined grids; and is the sensing matrix that shows the linear relation between and , and is composed of replicas (i.e., simulated pressures at the sensors with plane-wave approximation) for the predefined arrival angles as columns of .…”

Compressed sensing of impulse responses in rooms of unknown properties and contents

“…The success of CS relies on signal sparsity in a transform space (dictionary), and on a highly incoherent sensing operation. The benefit this framework has brought to the acoustics community is a reduction of microphones in various data acquisition and signal processing tasks [20], one of them being the task of interpolating RIRs. One of the pioneering papers was written by Mignot et al [21], in which a dictionary of virtual monopole sources is used to interpolate the early part of the RIRs -thereby exploiting the temporal sparsity of the early part, assuming the room is empty and there is no diffraction phenomena.…”