Optimization of a maximum entropy criterion for 2D Nuclear Magnetic Resonance reconstruction

This paper deals with the reconstruction of T1-T2 correlation spectra in Nuclear Magnetic Resonance (NMR) spectroscopy. The ill-posed character of this inverse problem and its large size are the main difficulties of the reconstruction. While maximum entropy is retained as an adequate regularization approach, the choice of an efficient optimization algorithm remains a challenging task. Our proposal is to apply a nonlinear conjugate gradient algorithm with two original features. Firstly, a theoretically well stated line search strategy suitable for the entropy function is applied to ensure a monotonic decrease of the criterion. Secondly, an appropriate preconditioning structure based on a truncated singular value decomposition of the forward model matrix is used to speed up the algorithm convergence. The resulting method reveals far more efficient than the classical Skilling and Bryan method and its applicability is illustrated through real NMR data processing.