Combination of compressed sensing and the optimum interpolation approximation: Theory and application for fast 2D NMR measurement

We present a new fast reconstruction method for 2D NMR spectrum by combining the compressed sensing (CS) method and the optimum interpolation approximation. We define a weighting function that has the same waveform of the 2D NMR spectrum reconstructed by the CS method. Then, the proposed method reconstructs the 2D NMR spectrum by the optimum interpolation approximation with the optimum interpolation functions derived from the weighting function. Experimental results show that the new method always reconstructs a more accurate 2D NMR spectrum for 101 different sampling patterns.