Reconstruction of jointly sparse signals using iterative hard thresholding

There is a recent interest in developing algorithms for the reconstruction of jointly sparse signals, which arises in a large number of applications such as sensor networks. In many of these applications, we encounter extremely large problem sizes for which algorithms with low computational complexity are required. Recently, an algorithm called iterative hard thresholding has been proposed, which is faster than the ℓ₁-minimization and greedy algorithms for compressed sensing. In this work, we extend the iterative hard thresholding algorithm to jointly sparse signals and will investigate the performance of our proposed algorithm analytically by giving conditions under which the exact reconstruction could happen. We will show that our algorithm is faster than the state of the art algorithms for jointly sparse signals while showing similar performance.