In compressed sensing, the common problem is to find the unique sparsest solution to an under-determined system of linear equations. The coefficients of this system are contained in the so called sensing matrix. Typical approaches consider this matrix to be random. However, deterministic constructions of such matrices may have promising features, like reconstruction performance guarantees, reduced memory requirements and less reconstruction complexity.
Recently, deterministic sensing matrices based on algebraic curves have been proposed. Their construction is an extension of a common approach by DeVore. The performance of these realizations varies with the realized dimensions.
In this thesis, the approach by DeVore and its extension to algebraic curves should be investigated. The construction should be further improved with respect to the abilities of the used reconstruction algorithm.