Recovery of Undersampled Sparse Signals using Combined Smoothed l_0l_1 Norm Compressed Sensing is a modern sampling technique that caught the attention of the scientific community due to its diverse applications. It accurately recovers sparse signalsimages from fewer samples that are well below the Nyquist Criterion. The linear recovery of undersampled sparse signalsimages is not possible using  l_2  norm minimization. The  l_2  norm based least squares linear recovery minimizes the total energy of the error resulting in a nonsparse solution. It is a proven fact that nonlinear  l_1  norm minimization promotes sparsity in the solution, which is desired in sparse signal recovery, however, it increases the computational complexity of the algorithm. The principal method for sparse signals reconstruction is based on  l_0  norm minimization that looks for a feasible solution having a minimum number of nonzeros and finding the solution to the  l_0  norm minimization is a combinatorial problem. There are nonlinear reconstruction techniques based on smoothed  l_0  and  l_1  norm approximations are proposed in the literature that are proven to be computationally efficient. In this research paper, the novel technique for recovery of a sparse signal is proposed, where  l_0  and  l_1  norm are combined to accurately recover compressively sampled sparse signals. The experimental results have shown that the proposed technique is more efficient than traditional smooth approximations of  l_0  and  l_1  norm.

An Efficient Approach for Image Resolution Enhancement Using Multi Step Magnification Method The lowresolution image is viewed as down sampled version of a highresolution image, whose patches are assumed to have a sparse representation with respect to an overcomplete dictionary of prototype signalatoms. The principle of compressed sensing ensures that under mild conditions, the sparse representation can be correctly recovered from the down sampled signal. We will demonstrate the effectiveness of sparsity as a prior for regularizing the otherwise illposed superresolution problem. We further show that a small set of randomly chosen raw patches from training images of similar statistical nature to the input image generally serve as a good dictionary, in the sense that the computed representation is sparse and the recovered high resolution image is competitive or even superior in quality to images produced by other SR methods.