Analysis of projection optimization in compressive sensing framework into reconstruction performance

Compressive Sensing (CS), which is firmly mathematically formulated by Danoho D, Candes E, Romberg J, and Tao T, is much developed especially for sensing and signal reconstruction. Its advantage framework on reducing number of measurement data while maintaining the performance of reconstruction quality, makes many researchers concern on developing the compressive sensing performance. The main parameters in CS are projection matrix and sparse base representation (dictionary). Subject to Restricted Isometric Property, the more incoherence between projection matrix and the dictionary, the more precise the signal reconstruction. Thus, a number of fundamental researches regarding projection optimization to optimize the incoherence between projection matrix and the dictionary have been developed. This paper elaborate the analysis of projection optimization's impact into reconstruction performance on signal with random and structured projection matrix. The simulations show that the projection optimization does not always imply better reconstruction especially for signal reconstruction with structured projection matrix.