  We propose a new algorithm for recovery of sparse signals from their
compressively sensed samples. The proposed algorithm benefits from the strategy
of gradual movement to estimate the positions of non-zero samples of sparse
signal. We decompose each sample of signal into two variables, namely "value"
and "detector", by a weighted exponential function. We update these new
variables using gradient descent method. Like the traditional compressed
sensing algorithms, the first variable is used to solve the Least Absolute
Shrinkage and Selection Operator (Lasso) problem. As a new strategy, the second
variable participates in the regularization term of the Lasso (l1 norm) that
gradually detects the non-zero elements. The presence of the second variable
enables us to extend the corresponding vector of the first variable to matrix
form. This makes possible use of the correlation matrix for a heuristic search
in the case that there are correlations among the samples of signal. We compare
the performance of the new algorithm with various algorithms for uncorrelated
and correlated sparsity. The results indicate the efficiency of the proposed
methods.
