Variable density compressed image sampling

Compressed sensing (CS) provides an efficient way to acquire and reconstruct natural images from a reduced number of linear projection measurements at sub-Nyquist sampling rates. A key to the success of CS is the design of the measurement ensemble. This paper addresses the design of a novel variable density sampling strategy, where the “a priori” information about the statistical distributions that natural images exhibit in the wavelet domain is exploited. Compared to the current sampling schemes for compressed image sampling, the proposed variable density sampling has the following advantages: 1) The number of necessary measurements for image reconstruction is reduced; 2) The proposed sampling approach can be applied to several transform domains leading to simple implementations. In particular, the proposed method is applied to the compressed sampling in the 2D ordered discrete Hadamard transform (DHT) domain for spatial domain imaging. Furthermore, to evaluate the incoherence of different sampling schemes, a new metric that incorporates the “a priori” information is also introduced. Extensive simulations show the effectiveness of the proposed sampling methods.