A new algorithm for the reconstruction of signals in compressive sensing framework is proposed. The algorithm is based on a least-squares method which incorporates a regularization to promote sparsity on the gradient of the signal. It uses a sequential basic conjugate-gradient method, and it is especially suited for the reconstruction of signals which exhibit temporal correlation, e.g., electrocardiogram (ECG) signals. Simulation results are presented which demonstrate that the proposed algorithm yields upto 80.28% reduction in mean square error and from 49.95% to 65.64% reduction in the required amount of computation, relative to the state-of-the-art block sparse Bayesian learning bound-optimization algorithm.
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