Acoustic contrast control with L1 constraint

Abstract

Optimal arrangement of loudspeakers in space is an important topic for the design of personal audio system with less number of loudspeakers. The acoustic contrast based on the ratio of acoustic energies(L2 norms) has been used for the maximization of sound pressure level difference between two different regions, but it only determines optimal driving functions of loudspeakers of which positions are fixed in advance. In this work, we aim at providing a means to determine the optimal loudspeaker locations by employing LI constraint to the optimization problem. The solution of L2 optimization calculated for possible candidate loudspeaker locations is given as an initial guess, and the general sparse eigenvalue problem is solved through iterations. The sparsity of the solution shows that the determination of optimal loudspeaker is possible in theory.