Variable Density Compressed Image Sampling

Compressed sensing (CS) provides an efficient way to acquire and reconstruct natural images from a limited number of linear projection measurements leading to sub-Nyquist sampling rates. A key to the success of CS is the design of the measurement ensemble. This correspondence focuses on the design of a novel variable density sampling strategy, where the a priori information of the statistical distributions that natural images exhibit in the wavelet domain is exploited. The proposed variable density sampling has the following advantages: 1) the generation of the measurement ensemble is computationally efficient and requires less memory; 2) the necessary number of measurements for image reconstruction is reduced; 3) the proposed sampling method can be applied to several transform domains and leads to simple implementations. Extensive simulations show the effectiveness of the proposed sampling method.