“…To obtain Figs 1 and 2, multiple snapshots are adopted. An example is also exhibited in Supplementary Note 1 to again demonstrate the advantages of the multiple-snapshot data model over the single-snapshot one, which has been demonstrated and explained in one- and two-dimensional fields 5,10,12,16,20 .Figure 1Microphone arrays and reconstructed source distributions. ( a ) The standard uniform cuboid microphone array for ( c , e and g ).…”
Section: Resultsmentioning
confidence: 81%
“…Differently, the methods in refs 13,14 are based on the single-snapshot data model, whereas the methods in this paper are based on the multiple-snapshot one. As proved by the literatures in one- and two-dimensional fields 5,10,12,16,20 , the multiple-snapshot method performs better. (3) In this paper, we deduce and develop an algorithm based on ADMM to solve the positive semidefinite programming, and demonstrate its advantage over the IPM based SDPT3 solver.…”
Section: Introductionmentioning
confidence: 80%
“…16 extended Xenaki et al .’s beamformer to the multiple-snapshot case via the group atomic norm. The authors 17–20 developed a two-dimensional single-snapshot continuous compressive beamformer for the measurement with rectangular microphone arrays based on the minimization of the atomic norm of microphone signal induced by sources and the matrix enhancement and matrix pencil method 21 , and extended it to the multiple-snapshot case via the group atomic norm and the matrix pencil and pairing (MaPP) method 13,14 . Treating the DOAs of sources as a continuum, these beamformer can sidestep the basis mismatch conundrum fundamentally.…”
Section: Introductionmentioning
confidence: 99%
“…Treating the DOAs of sources as a continuum, these beamformer can sidestep the basis mismatch conundrum fundamentally. Moreover, the multiple-snapshot data help to obtain more accurate and robust results compared with the single-snapshot ones 16,20 . In the linear array, there are only a line of microphones.…”
Compressive beamforming is a powerful approach for the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. The conventional grid-based discrete compressive beamformer suffers from the basis mismatch conundrum. Its result degrades under the situation that sources fall off the grid. The existing continuous compressive beamformer with linear or planar microphone arrays can circumvent the conundrum, but work well only for sources in a local region. Here we develop a panoramic continuous compressive beamformer with cuboid microphone arrays based on an atomic norm minimization (ANM) and a matrix pencil and paring method. To solve the positive semidefinite programming equivalent to the ANM efficiently, we formulate a solving algorithm based on the alternating direction method of multipliers. We also present an iterative reweighted ANM to enhance sparsity and resolution. The beamformer is capable of estimating the DOAs and quantifying the strengths of acoustic sources panoramically and accurately, whether a standard uniform or a sparse cuboid microphone array is utilized.
“…To obtain Figs 1 and 2, multiple snapshots are adopted. An example is also exhibited in Supplementary Note 1 to again demonstrate the advantages of the multiple-snapshot data model over the single-snapshot one, which has been demonstrated and explained in one- and two-dimensional fields 5,10,12,16,20 .Figure 1Microphone arrays and reconstructed source distributions. ( a ) The standard uniform cuboid microphone array for ( c , e and g ).…”
Section: Resultsmentioning
confidence: 81%
“…Differently, the methods in refs 13,14 are based on the single-snapshot data model, whereas the methods in this paper are based on the multiple-snapshot one. As proved by the literatures in one- and two-dimensional fields 5,10,12,16,20 , the multiple-snapshot method performs better. (3) In this paper, we deduce and develop an algorithm based on ADMM to solve the positive semidefinite programming, and demonstrate its advantage over the IPM based SDPT3 solver.…”
Section: Introductionmentioning
confidence: 80%
“…16 extended Xenaki et al .’s beamformer to the multiple-snapshot case via the group atomic norm. The authors 17–20 developed a two-dimensional single-snapshot continuous compressive beamformer for the measurement with rectangular microphone arrays based on the minimization of the atomic norm of microphone signal induced by sources and the matrix enhancement and matrix pencil method 21 , and extended it to the multiple-snapshot case via the group atomic norm and the matrix pencil and pairing (MaPP) method 13,14 . Treating the DOAs of sources as a continuum, these beamformer can sidestep the basis mismatch conundrum fundamentally.…”
Section: Introductionmentioning
confidence: 99%
“…Treating the DOAs of sources as a continuum, these beamformer can sidestep the basis mismatch conundrum fundamentally. Moreover, the multiple-snapshot data help to obtain more accurate and robust results compared with the single-snapshot ones 16,20 . In the linear array, there are only a line of microphones.…”
Compressive beamforming is a powerful approach for the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. The conventional grid-based discrete compressive beamformer suffers from the basis mismatch conundrum. Its result degrades under the situation that sources fall off the grid. The existing continuous compressive beamformer with linear or planar microphone arrays can circumvent the conundrum, but work well only for sources in a local region. Here we develop a panoramic continuous compressive beamformer with cuboid microphone arrays based on an atomic norm minimization (ANM) and a matrix pencil and paring method. To solve the positive semidefinite programming equivalent to the ANM efficiently, we formulate a solving algorithm based on the alternating direction method of multipliers. We also present an iterative reweighted ANM to enhance sparsity and resolution. The beamformer is capable of estimating the DOAs and quantifying the strengths of acoustic sources panoramically and accurately, whether a standard uniform or a sparse cuboid microphone array is utilized.
“…Also, the theorem is applied using the conventional sparse beamforming approach, which is subject to the problem of basis mismatch. Thus, aliasing-free localization using the grid-free method [111] will be an interesting direction to study and bridge the research gap between Chapters 3 and 4.…”
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