Mathematics Approaches in Compressed Sensing

Abstract

Mathematical approaches refer to make quantitative descriptions, deductions and calculations through the use of mathematics concepts, approaches and techniques, then draw some new conclusions and foresee by mathematical analysis and judgment. In recent years, Compressed Sensing theory (CS) provides solutions in alleviating the huge amount of information demand in the pressure of signal sampling, transmission and storage pressure. It is a novel signal sampling theory under the condition that the signal is compressible or sparse.In this case, the signal can be reconstructed accurately from the small amount of signal values if the signal is sparse or compressible. This paper introduces the CS theory framework and key technical issues, and focus on the analysis of the application of mathematical approaches in three aspects of the signal sparse representation, signal sparse transformation and reconstruction.In the end, Some mathematics problems of compressed sensing to solve are given and further development is pointed out.

DOI: http://dx.doi.org/10.11591/telkomnika.v11i9.3303