Empirical analysis of the C-value in the conditional inequality of dimension of measurement matrix in compressive sensing

Standard CS (Compressive Sensing) indicates the number of the samples which should be taken from the original signal in the sender to be reconstructed in the receiver is M ≥ CKμ log N. In the inequality, all of the variables can be known except for C. This paper mainly discusses the factors that influence this variable. Our contributions can be concluded into two aspects: firstly, we conclude that the length N and the sparsity K of the original signal are not the main factors that influence C and it is influenced by the type of measurement matrix and reconstruction algorithm; secondly, we provide the lower bound of C which can be used in practice to reconstruct the original signal with high precision.