Multichannel active noise control for spatially sparse noise fields

Multi-channel active noise control (ANC) is currently an attractive solution for the attenuation of low-frequency noise fields, in three-dimensional space. This paper develops a controller for the case when the noise source components are sparsely distributed in space. The anti-noise signals are designed as in conventional ANC to minimize the residual errors but with an additional term containing an ℓl norm regularization applied to the signal magnitude. This results in that only secondary sources close to the noise sources are required to be active for cancellation of sparse noise fields. Adaptive algorithms with low computational complexity and faster convergence speeds are proposed.