High-Resolution Signal and Noise Field Estimation Using the 1 (Least Absolute Values) Norm

In this paper a new method for obtaining a quantitative estimate of an acoustic field consisting of a set of discrete sources and background noise is described. The method is based on the 1 (least absolute values) norm solution to an underdetermined system of linear equations defining the Fourier transform of the signal series. Implementations of the method with either equality or inequality constraints are presented and discussed. The much faster and more compact equality constraint version with a provision for modeling the noise field is recommended in practice. Experience with real data has shown the necessity of correcting for an observed Gaussian decay on the covariances. A simple means of estimating this effect and taking it into account in the signal estimation procedure is discussed, and the implications of this effect in high-resolution beamforming are considered. The effectiveness and versatility of the 1 method indicate that it has a useful role in high-resolution signal estimation.