Non-uniform sampling in multidimensional NMR shows great promise to significantly decrease experimental acquisition times, especially for relaxation experiments for which peak locations are already known. In this paper we present a method for optimizing the non-uniform sampling points such that the noise amplification and numerical instabilities are minimized. In particular, the minimum singular value of the Moore-Penrose pseudo-inverse is maximized using sequential semi-definite programming, thereby minimizing the worst-case errors. We test this method numerically on a set of assignment data from the proteins ubiquitin (in both folded and unfolded states) and RIalpha (119-244), a cAMP-binding regulatory subunit of protein kinase A (PKA). This test indicates that optimizing more than doubles the efficiency over random selection of points, and the efficiency increases as we go to higher dimensions.
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