||Sound Source Reconstruction with Covariance Matrix Fitting
||Lange, Katrine (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Hansen, Per Christian (Scientific Computing, Institut for Informatik og Matematisk Modellering, Danmarks Tekniske Universitet, DTU, DK-2800 Kgs. Lyngby, Denmark)
Jørgensen, John Bagterp (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||This thesis is a feasibility study of Covariance Matrix Fitting (CMF) as a Beamforming
technique. The main focus will be on improving the quality of the
computed solutions by introduction of a regularization term as well as on implementation
of an efficient solution algorithm.
It is shown how the problem can be formulated as a convex, quadratic programming
problem and a reduced formulation is derived to significantly reduce the
computational cost of forming the problem.
Relevant theory from inverse problems and optimization is presented. The
regularization methods Tikhonov regularization and Total Variation regularization
are described and the corresponding regularized CMF Beamforming problems
are derived. The ill-conditioned nature of the CMF Beamforming problem
is discussed and the need of regularization at the lower frequencies documented
and sought fullfilled.
A primal-dual interior-point algorithm is implemented tailored to solve the
Tikhonov regularized CMF Beamforming problem. The algorithm exploits the
matrix structure of the problem and a modified search direction is proposed to
reduce computation cost.
Simulated and real test data are used to illustrate the general quality of the
computed solutions as well as how regularization improves the quality of the
computed solutions in the severely ill-posed cases.
||Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Creation date: 2010-04-16
Update date: 2010-10-28