Sound Field Decomposition Using SPICE Decomposition

Abstract

We propose a method to estimate a reverberant sound field by compressed sensing approach without using the hyper parameter for controlling sparsity. This method first applies sparse iterative covariance-based approach (SPICE) to the power spectral density matrix of the microphone signals and obtains the estimate of sensor noise power without using a hyper parameter. From this estimate, a convex optimization problem for a sparse solution is obtained that relates the microphone signals, plane-wave expansion coefficients, and the sensor noise power. The plane-wave expansion coefficients are obtained as the solution of this convex optimization problem. The sound field can be estimated from the plane-wave expansion coefficients.