Maximum entropy regularization for Fredholm integral equations of the first kind
SIAM Journal on Mathematical Analysis
Line search algorithms with guaranteed sufficient decrease
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
Journal of Optimization Theory and Applications
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A survey of truncated-Newton methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
On the Complexity of a Practical Interior-Point Method
SIAM Journal on Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Solving Fredholm integrals of the first kind with tensor productstructure in 2 and 2.5 dimensions
IEEE Transactions on Signal Processing
An Expanded Theoretical Treatment of Iteration-Dependent Majorize-Minimize Algorithms
IEEE Transactions on Image Processing
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This paper deals with the reconstruction of T1-T2 correlation spectra in nuclear magnetic resonance relaxometry. The ill-posed character and the large size of this inverse problem are the main difficulties to tackle. 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 truncated Newton algorithm with two original features. First, a theoretically sound line search strategy suitable for the entropy function is applied to ensure the convergence of the algorithm. Second, an appropriate preconditioning structure based on a singular value decomposition of the forward model matrix is used to speed up the algorithm convergence. Furthermore, we exploit the specific structures of the observation model and the Hessian of the criterion to reduce the computation cost of the algorithm. The performances of the proposed strategy are illustrated by means of synthetic and real data processing.