A Noise-Robust Method with Smoothed ℓ/ℓRegularization for Sparse Moving-Source Mapping

Mai Quyen Pham, Benoit Oudompheng, Jérôme I. Mars, Barbara Nicolas

Abstract: The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smoothed ℓ1/ℓ2<math><mrow is="true"><msub is="true"><mrow is="true"><mo is="true">ℓ</mo></mrow><mrow is="true"><mn is="true">1</mn></mrow></msub><mo is="true">/</mo><msub is="true"><mrow is="true"><mo is="true">ℓ</mo></mrow><mrow is="true"><mn is="true">2</mn></mrow></msub></mrow></math> regularization term. As the mean of the noise in the power spectrum domain depends on its variance in the time domain, the proposed method includes a variance estimation step, which allows more robust blind deconvolution. Validation of the method on both simulated and real data, and of its performance, are compared with two well-known methods from the literature: the deconvolution approach for the mapping of acoustic sources, and sound density modeling.