Compressed sensing with partial support information: coherence-based performance guarantees and alternative direction method of multiplier reconstruction algorithm

The recently introduced theory of compressed sensing (CS) enables the recovery of sparse or compressible signals from a small set of non-adaptive measurements, and furthermore, it holds promise for substantially improving the performance by leveraging more signal structures that go beyond simple sparsity. In this study, the authors study the weighted l₁ minimisation problem for CS reconstruction when partial support information is available. Firstly, they focus on the coherence-based performance guarantees and show that if an estimated support can be obtained with its accuracy and relative size satisfying certain coherence-related conditions, the weighted l₁ minimisation is then stable and robust under weaker sufficient conditions than that of the analogous standard l₁ optimisation. Meanwhile, better upper bounds on the reconstruction error could also be achieved. Besides, a novel adaptive alternating direction method of multipliers with iterative support detection is outlined to solve the weighted l₁ minimisation problem. Simulation results show that the authors´ method achieves good convergence, and obtains improved reconstruction performance in comparison with the conventional methods.