Study on Joint Semi-Iterative Hard Thresholding Pursuit Algorithm in Mixed Support-set Model

In wireless sensor networks, the mixed support-set model can provide additional degrees of freedom for network frame since it has no constraint on the common signal components. With respect to the high stability and robustness property of modified Semi-Iterative Hard Thresholding Pursuit algorithm (SHTP) in -norm convex optimization, we propose a joint SHTP reconstruction algorithm by combining SHTP algorithm with the mixed support-set model to realize the distributed compressed sensing of the signal groups in a multiple-sensor setup where all the sensors transmit the sensing data to the centralized node. The algorithm aims at solving a common sparse signal part utilizing the inter-signal correlation to gain a common support set as the initial values, based on which the individual signal part can be reconstructed using the inner-signal correlation. The simulation results show that, compared with the existed joint reconstruction algorithms, such as joint OMP and joint SP, the joint SHTP algorithm could gain the maximum signal to reconstruction noise ratio and the minimum average support cardinality error. It is indicated that the proposed algorithm can achieve the precise reconstruction no matter the network setup is noisy or not.