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We propose a new algorithm for recovery of sparse signals from theircompressively sensed samples. The proposed algorithm benefits from the strategyof gradual movement to estimate the positions of non-zero samples of sparsesignal. We decompose each sample of signal into two variables, namely "value"and "detector", by a weighted exponential function. We update these newvariables using gradient descent method. Like the traditional compressedsensing algorithms, the first variable is used to solve the Least AbsoluteShrinkage and Selection Operator (Lasso) problem. As a new strategy, the secondvariable participates in the regularization term of the Lasso (l1 norm) thatgradually detects the non-zero elements. The presence of the second variableenables us to extend the corresponding vector of the first variable to matrixform. This makes possible use of the correlation matrix for a heuristic searchin the case that there are correlations among the samples of signal. We comparethe performance of the new algorithm with various algorithms for uncorrelatedand correlated sparsity. The results indicate the efficiency of the proposedmethods.

Gradually Atom Pruning for Sparse Reconstruction and Extension to Correlated Sparsity