Noise reduction by a new iterative weighted sparse decomposition algorithm

In this paper, a new weighted sparse decomposition algorithm is developed for signal recovery from noisy recordings. The algorithm is completed by iteratively solving the global minimum l₁ norm to seek the sparse component of the signal in a complete or over-complete dictionary, in order to get an estimate of the signal. The multiresolution wavelet is adopted as the complete dictionary, and the two-scale relation in wavelet algorithm was utilized to define the penalty parameter in the objective function. The method is confirmed by both simulation and real data.