A theoretical analysis of the DAMAS algorithm proposed by Brooks and Humphreys is introduced, with the main result that the DAMAS algorithm converges towards a solution of a convex problem, that is equivalent to a non-negative least squares fitting of a diagonal covariance matrix to the data. Properties of solutions of this optimization problem support the observation that the DAMAS algorithm is able to recover sparse distributions of sources, even without a regularization term. Additionally, using this new characterization of limit points of the DAMAS algorithm and an efficient implementation of the Lawson-Hanson algorithm, source powers can be estimated efficiently for large scale problems, both in memory and computational time. An application to a large-scale 3D problem with experimental data demonstrates the numerical efficiency of the proposed method, and simulations are used to assess the performances of source power estimation.
Demo : damas.zip (Matlab/Octave and python code).
Generates the figures of the paper, and demo code on a simple case.