Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices
  We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss functions. Numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method. 
Dan Yang, Zongming Ma, Andreas Buja
math.ST stat.TH