Abstract
In compressive sampling matching pursuit algorithm, it requires that the sparsity information of original signal to control the size of the preliminary atomic set and the maximum number of the algorithm iteration. This weakens the reconstruction accuracy, increases the computation complexity and limits its practical application capacity. To overcome the problem, an improved method is proposed. The proposed method firstly sets a fixed step-size as the assumed sparsity to expand the preliminary atomic set at the initial stage when the sparsity information is unknown. Secondly, the proposed algorithm adopts the fuzzy threshold strategy to select the more relevant atoms from the preliminary atomic set to expand the candidate atomic set. Finally, the double threshold control method, multiply stages setting and variable step-size method are used to control the iteration stop condition and adjust the estimated sparsity. When the two threshold iteration stop conditions are simultaneously satisfied, the iteration stops, which shows that the reconstructed signal better approximated the original signal, and the reconstruction performance is the best. Otherwise, if only one of the conditions is satisfied, the size of the estimated sparsity is increased by the variable step size method to reduce the error between the reconstructed signal and original signal. In addition, we extended the proposed algorithm to the multiple measurement vectors scenario for joint sparse signal recovery. Simulation results indicate that the proposed algorithm is better than the other method in terms of the reconstruction performance in single measurement vector and multiple measurement vector cases.
Highlights
Compressed sensing (CS) [1] is a novel signal compression and processing theory
Compared with the Nyquist sampling theory, the most important of CS theory is that it can be randomly sampled by standards that are far less than Nyquist’s, and the original signal can be recovered under small distortion rates
We propose a double threshold control method and multiple stage variable step-size method to control the convergence condition of the algorithm and adjust the estimated sparsity, thereby getting rid of the dependency of sparsity information of original signal
Summary
Compressed sensing (CS) [1] is a novel signal compression and processing theory. Compared with the Nyquist sampling theory, the most important of CS theory is that it can be randomly sampled by standards that are far less than Nyquist’s, and the original signal can be recovered under small distortion rates. The multiple measurement vectors (MMV) model is extended to compressed sensing theory to solve the jointly sparse recovery problem [18]–[22]. W ∈ RM×1 denotes that the additive noise vector, and which is usually Gaussian white noise This reconstruction problem, approximately estimating x from (2) using the measurement matrix and the observing vector, is known as the SMV problem. Top-down methods such as SP and CoSaMP use the backtracking strategy to more accurately determine the true support set of atoms, and the final solution of the signal is obtained by the least squares methods. The CoSaMP algorithm requires that the sparsity of the signal is known, and uses the size of the sparsity to set the number of selected atoms. We deduce the proposed method for SMV model and MMV model, respectively
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