Near-field acoustic holography using sparse regularization and compressive sampling principles

Abstract

Regularization of the inverse problem is a complex issue when using near-field acoustic holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, alternative regularization schemes can be developed based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e., the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of compressive sampling; under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

“…Exploiting the underlying sparsity, sparse signal reconstruction improves significantly the resolution in DOA estimation. [9][10][11][12] While ' pnorm regularized maximum likelihood methods, with p 1, have been proposed to promote sparsity in DOA estimation [9][10][11]13 and wavefield reconstruction, 14,15 the accuracy of the resulting sparse estimate is determined by the ad hoc choice of the regularization parameter. 12,16 Sparse Bayesian learning (SBL) is a probabilistic parameter estimation approach which is based on a hierarchical Bayesian method for learning sparse models from possibly overcomplete representations resulting in robust maximum likelihood estimates.…”

Dictionary-based Equivalent Source Method for Near-Field Acoustic Holography

“…Then, the vibration mode at w is given by the surface normal velocity at B discrete points on the object surface, estimated as [9] v(w) = G v(w)q(w) , (5) where SI , . .. , SB are the surface points coordinates, b = 1, ... , B ; nb denotes the unit vector normal to the surface at Sb.…”

“…The groundtruth plate velocity, measured by means of a laser vibrometer, is also provided. Details ab out the acquisition setup can be found in [5].…”

“…proposed in [5], where vibration modes of star-shaped planar plates are described by a linear combination of plane-waves components. Using this model, the solution to the NAH problem is approximated using a compressive sampling approach, finding a sparse solution in the space spanned by plane-wave basis functions.…”

Block-sparse beamforming for spatially extended sources in a Bayesian formulation

“…Regularization with the ' 2 -norm is also typical in near-field acoustical holography (NAH) methods for sound field reconstruction. 2,3 Since there are usually only a few sources, regularization with the ' 1 -norm 4,5 attracts increasing attention [6][7][8][9][10][11][12][13][14][15][16] as it provides high-resolution DOA reconstruction due to its sparsity promoting characteristics. In underwater acoustics, using multiple constraints to account for simultaneous characteristics of the solution as sparsity and smoothness (i.e., ' 1 -norm and ' 2 -norm) is shown to improve the resolution of shallow-water source localization with matched-field processing.…”