Image Compressive Sensing Based on Blended Basis Functions

Compressive sensing (CS) has given us a new idea at data acquisition and signal processing. It has proposed some novel solutions in many practical applications. Focusing on the image compressive sensing problem, the paper proposes an algorithm of compressive image sensing based on the multi-resolution analysis. We present the method to decompose the images by nonsubsampled contourlet transform (NSCT) and wavelet transform successively. It means that the images can be sparse represented by more than one basis functions. We named this process as blended basis functions representation. Since the NSCT and wavelet basis functions have complementary advantages in the image multi-resolution analysis, and the signals are more sparse after decomposed by two kinds of basis functions, the proposed algorithm has perceived advantages in comparison with compressive sensing in the wavelet domain which is widely reported by literatures. The simulations show that our method provides promising results.