Wednesday, August 15, 2012, 2:00 pm
Uni West, Room 43.2.101
The principle of Compressed Sensing (CS) allows to find the unique sparsest solution of an under-determined system of linear equations over the field of real numbers. This is commonly used for the acquisition of a sufficiently sparse vector of real-valued data by small number of measurements determined by a properly chosen measurement matrix. The most common method for reconstruction of sparse vectors in a polynomial time is the well-known Basis Pursuit (BP) algorithm.
The objectives of this thesis are the introduction of CS with a special focus on the properties of the measurement matrix allowing successful reconstruction of a sparse vector by the BP algorithm, description of best spherical codes and their implementation for the construction of measurement matrices, as well as numerical evaluations and comparisons of CS-properties of measurement matrices based on spherical codes.