A Fast Reconstruction Method for Approximately Sparse Signal in Compressed Sensing

The fast and accurate reconstruction of approximately sparse signal in compressed sensing is investigated. A new method of ASL₀ (smoothed l₀ norm with analysis) is proposed based on analysis model and SL₀. Analysis approach can avoid the accumulative errors caused by synthesis approach, and the smoothed l₀ norm makes the optimization process simpler. The simulation results on one-dimension piece-wise smooth signals demonstrate that ASL₀ can reconstruct the signal accurately and lower the computational complexity, which shows ASL₀ method is suitable to be used to reconstruct the approximately sparse signals.