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A New Method for Sparse Signals Reconstruction in Fusion Center with Incomplete Measurements

In this paper, we focus on a specific problem in joint sparse signals recovery, where not all of the measurements are fully received (observed) in the data fusion center (FC), but some of them are missing. Most of the previous work focused on the sparse signals recovery problem that the information of the measurements in FC is complete (fully observed). However, in practice, usually it is not easy for the data center to receive complete measurements, due to limited sampling rate, noise corruption, or transmission error, etc. Hence, how to reconstruct the sparse signals under the incomplete measurements is an important problem for the fusion center. Based on Regularized M-FOCUSS (FOCal Underdetermined System Solver) algorithm, this paper proposes a new method to efficiently reconstruct the sparse signals from the incomplete measurements. Different to the widely used matrix completion based method, our method obtains the solution from the received measurements directly, instead of running the matrix completion algorithm in advance. Furthermore, our method shows excellent recovery performance compared to the matrix completion based method, and also the independent vector recovery method, and the block-sparse based recovery method. Experimental results are also provided to show the effectiveness of our proposed scheme.