Sparseness-Aware DOA Estimation with Majorization Minimization

Refinement of Direction of Arrival Estimators by Majorization-Minimization Optimization on the Array Manifold

“…From this estimate, they obtain a basis E k for the noise subspace at f k and the DOA is obtained from (3) with C k = E k E H k and s = −1. Robust Speech DOA Methods, e.g., [29,30,21], are robust DOA estimators exploiting the sparseness of speech signals. Namely, they assume so-called W-disjoint orthogonality whereas each time-frequency bin is occupied by at most one source.…”

“…By the method of Lagrange multipliers, the solution is q t = q(µ0) = (D+µ0I) −1 v, where µ0 is the unique zero of q(µ) 2 −1 larger than −λmin, with λmin the smallest eigenvalue of D. The zero can be efficiently found by Newton-Raphson or bisection, and working in the eigenspace of D (see [24,21] for details).…”

“…Due to the norm constraint q q = 1, the quadratic term becomes constant and we obtain (21). Now, the corresponding MM update is given by solving (12) for v = 1.…”

“…We formulate the problem as the minimization of the power mean [23] of the cost at the different frequency bands. We produce two surrogate functions, one quadratic, similar to [21], and one linear. The former can be minimized efficiently by the generalized trust region sub-problem method [24], as in [21], and the latter has a closed-form solution.…”

“…We produce two surrogate functions, one quadratic, similar to [21], and one linear. The former can be minimized efficiently by the generalized trust region sub-problem method [24], as in [21], and the latter has a closed-form solution. Both lead to iterative algorithms that are guaranteed to decrease the value of the objective.…”