531 research outputs found
Nearfield Acoustic Holography using sparsity and compressive sampling principles
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, new 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 new 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.Comment: Journal of the Acoustical Society of America (2012
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