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This paper investigates sound-field modeling in a realistic reverberant setting. Starting from a few point-like microphone measurements, the goal is to estimate the direct source field within a whole three-dimensional (3-D) space around these microphones. Previous sparse sound field decompositions assumed only a spatial sparsity of the source distribution, but could generally not handle reverberation. We here add an explicit model of the reverberant sound field, that has two components: the first component sparse in the plane-wave domain, the other component low-rank as a multiplication of transfer functions and source signals. We derive the corresponding decomposition algorithm based on the alternating direction method of multipliers. We furthermore provide empirical rules for tuning the two parameters to be set in the algorithm. Numerical and experimental results indicate that the decomposition and reconstruction performances are significantly improved, in the case of reverberant environments.
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