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We introduce a two step algorithm with theoretical guarantees to recover ajointly sparse and low-rank matrix from undersampled measurements of itscolumns. The algorithm first estimates the row subspace of the matrix using aset of common measurements of the columns. In the second step, the subspaceaware recovery of the matrix is solved using a simple least square algorithm.The results are verified in the context of recovering CINE data fromundersampled measurements; we obtain good recovery when the sampling conditionsare satisfied.

Two step recovery of jointly sparse and low-rank matrices: theoretical guarantees