Compress Sensing
A. Vakili; M. Shams Esfand Abadi; M. Kalantari
Abstract
Background and Objectives: In the realm of compressed sensing, most greedy sparse recovery algorithms necessitate former information about the signal's sparsity level, which may not be available in practical conditions. To address this, methods based on the Sparsity Adaptive Matching Pursuit (SAMP) algorithm ...
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Background and Objectives: In the realm of compressed sensing, most greedy sparse recovery algorithms necessitate former information about the signal's sparsity level, which may not be available in practical conditions. To address this, methods based on the Sparsity Adaptive Matching Pursuit (SAMP) algorithm have been developed to self-determine this parameter and recover the signal using only the sampling matrix and measurements. Determining a suitable Initial Value for the algorithm can greatly affect the performance of the algorithm.Methods: One of the latest sparsity adaptive methods is Correlation Calculation SAMP (CCSAMP), which relies on correlation calculations between the signals recovered from the support set and the candidate set. In this paper, we present a modified version of CCSAMP that incorporates a pre-estimation phase for determining the initial value of the sparsity level, as well as a modified acceptance criteria considering the variance of noise. Results: To validate the efficiency of the proposed algorithm over the previous approaches, random sparse test signals with various sparsity levels were generated, sampled at the compression ratio of 50%, and recovered with the proposed and previous methos. The results indicate that the suggested method needs, on average, 5 to 6 fewer iterations compared to the previous methods, just due to the pre-estimation of the initial guess for the sparsity level. Furthermore, as far as the least square technique is integrated in some parts of the algorithm, in presence of noise the modified acceptance criteria significantly improve the success rate while achieving a lower mean squared error (MSE) in the recovery process.Conclusion: The pre-estimation process makes it possible to recover signal with fewer iterations while keeping the recovery quality as before. The fewer the number of iterations, the faster the algorithm. By incorporating the noise variance into the accept criteria, the method achieves a higher success rate and a lower mean squared error (MSE) in the recovery process.
