Complex-valued Reed-Solomon Codes for Deterministic Compressed Sensing

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We propose to investigate the application of Reed-Solomon codes over the complex numbers (CRS) as deterministic Compressed Sensing (CS) schemes. Recent research results in decoding RS codes over finite fields and complex numbers can be studied for their usage in CS. Deterministic CS schemes offer (non-probabilistic) reconstruction guarantees, reduced storage requirements or less complex computation by utilizing the structure embedded into the deterministic sensing matrix. However, the existing decoding algorithms for RS codes need to be adapted to the problems arising with the usage of the complex field and the implementation with finite precision. Especially the robustness of the algorithms against non-sparse distortions is an important additional factor which needs to be considered. First results on CRS-based CS schemes are promising.