Coherence Based Trajectory Optimization for Compressive Sensing of Sound Fields

Moving microphones allow for the fast acquisition of spatially dense sound-field data. The dynamic samples encode parameters that describe the particular sound field. For parameter decoding, a deconvolution problem in the time dimension and an interpolation problem in the spatial dimension must be solved simultaneously. The corresponding system of linear equations tends to be ill-posed and underdetermined unless an excessive number of samples is provided. Therefore, sparse recovery according to the compressed-sensing paradigm is required, which is achievable by exploiting the sparsity of sound fields in frequency domain. At this, stability and robustness depend on the sensing matrix and can be indicated by its coherence. For optimizing the coherence, mathematical tools that operate directly on the sensing matrix are impractical, as the dynamic-sensing matrix possesses structured entries constrained by the measurement trajectory. In this paper, we present an efficient update scheme that allows for the direct manipulation of the microphone trajectory for improving the coherence of the sensing matrix and, thus, reducing error bounds of the sparse recovery in frequency domain.