Two step recovery of jointly sparse and low-rank matrices: theoretical   guarantees
  We introduce a two step algorithm with theoretical guarantees to recover a jointly sparse and low-rank matrix from undersampled measurements of its columns. The algorithm first estimates the row subspace of the matrix using a set of common measurements of the columns. In the second step, the subspace aware recovery of the matrix is solved using a simple least square algorithm. The results are verified in the context of recovering CINE data from undersampled measurements; we obtain good recovery when the sampling conditions are satisfied. 
Sampurna Biswas, Sunrita Poddar, Soura Dasgupta, Raghuraman Mudumbai   and Mathews Jacob
stat.ML cs.IT math.IT