Sparse modal estimation of 2-D NMR signals

We propose a sparse modal estimation approach for analyzing 2-D NMR signals. It consists in decomposing the 2-D problem into two 1-D modal estimations. Each 1-D problem is formulated in terms of simultaneous sparse approximation which is efficiently solved using the Simultaneous Orthogonal Matching Pursuit method associated with a multi-grid dictionary refinement. Then, we propose a new criterion for mode pairing which comes down to solve a sparse approximation problem involving a low dimensional dictionary. The effectiveness of the method is demonstrated on real NMR data.