Image sparsity evaluation based on principle component analysis

In compressive sensing, signal sparsity is an important parameter which influences the number of data sampling in reconstruction process and the quantity of the reconstructed result. But in practice, undersampled and oversampled phenomenon will occur because of the unknown sparsity, which may lose the advantages of compressive sensing. So how to determine the image sparsity quickly and accuratly is significant in the compressive sensing process. In this paper, we calculate the image sparsity based on the data acquired during compressive sensing recontruction projection which sparses the origin image in wavelets domain, but we find that its procession is complex, and the final results are seriously influenced by wavelet basis function and the transform scales. We then introduce the principle component analysis (PCA) theory combined with compressive sensing, and establish a linear relationship between image sparsity and coefficient founction variance based on the assumption that PCA is of approximately normal distribution. Multiple sets of experiment data verify the correctness of the linear relationship mentioned above. Through previous analysis and simulation, the sparsity estimation based on PCA has an important practical value for compressive sensing study.