Research On Signal Reconstruction Algorithms Based On Compressed Sensing

The sampling rate must be two times higher than the highest frequency of the signal based on Nyquist sampling theorem. When the frequency of the signal is too high, there will be too many sampling points to process and transmit. Recently, a new sampling theorem has been proposed-compressed sensing. For sparse and compressive signal, the sampling rate based on CS can be very lower than the sampling rate based on Nyquist. This is because that it compress the signal when sampling it. The signal can be reconstructed exactly by using the appropriate reconstruction algorithms. The reconstruction algorithm is the key point that most researchers focus on and significant progress has been made. The paper will focus on the following parts:1) Improvements on Gradient Pursuit algorithm for signal reconstruction based on CSGradient Pursuit (GP) algorithm is one kind of the Greedy Algorithms for signal reconstruction. It is a practical method as a result of less computational requirements and better performance for signal reconstruction. GP algorithm is based on the steepest descent method of optimization theory. It uses the steepest descent step-size for the iterative reconstruction, which leads to the zigzag phenomenon and slow convergence. In the paper, improvements on the step-size for the original gradient pursuit algorithm are proposed by introducing Alternating Step-size (AS) and Shortened Step-size (SS). The experimental results show that the new method is superior to the available gradient pursuit method.2) Improvement on CMP algorithm for signal reconstruction based on CSMost of the reconstruction algorithms reconstruct the original signal from the measured signal y and sensing matrixφof M-dimension. Recently Rath and Guillemot proposed the complementary matching pursuit (CMP) algorithm which is similar to the matching pursuit, but is performed in the original signal space of N-dimension rather than the measured signal space of M-dimension. The simulation results show that the convergence speed and the reconstruction quality are both improved by performing the approximations in the original signal space. In the paper, we combine the advantages of both GP and CMP algorithms and propose a new method which needs less computation time but have better performance compared to other improved algorithms of original CMP. 3) A new method for sparsity estimationMany practical and efficient reconstruction algorithms need the prior knowledge about the sparsity of signal, but actually we don't have the information about it. Recently a method for sparsity estimation has been proposed. But the method is not so efficient because the zero is used as an initial value, and also it is combined to Subspace Pursuit algorithm, that means, the adjustment of sparsity estimation is in the SP algorithm iterative steps, so this estimation method can't be used to other algorithms. In the paper, improvements on these two defects are proposed. First, the initial value of sparsity will begin from a suitable value which is between the (0～0.1)M.Then we will use a threshold to adjust the sparsity we have estimated and this adjustment is independent from the reconstruction algorithms. The sparsity estimated by this method is almost the exact one and can be applied to all the algorithms which need it.