Image reconstruction from incomplete measurements: Maximum Entropy versus L1 norm optimization

Maximum Entropy (MaxEnt) and Compressive Sensing (CS) are two paradigms that allow good image reconstruction from a low number of measurements. MaxEnt is based on the maximization of entropy while CS uses the minimization of l₁ norm of image sparse representation. In this paper, MaxEnt and CS are tested in conditions simulating the acquisition by Single Pixel Camera. The set of measurements is obtained by non-uniform sampling (NUS) of the image. Before sampling, the images are blurred with a Gaussian kernel in order to simulate the camera Point Spread Function (PSF). The results show that both CS and MaxEnt reconstruct above the quality of blurred image and that, generally, CS performs better than MaxEnt. The impact of sparsity and camera PSF are discussed. The sparsity has higher influence in CS than in MaxEnt while for the PSF, it is the opposite: CS does not seem to be sensitive to the PSF size. The number of measured samples is also discussed. For more than 50% measured pixels, MaxEnt improves only a few the image quality while CS increases constantly the image PSNR.