Regularization methods in dynamic MRI

In this work we consider an inverse ill-posed problem coming from the area of dynamic magnetic resonance imaging (MRI), where high resolution images must be reconstructed from incomplete data sets collected in the Fourier domain. The reduced-encoding imaging by generalized-series reconstruction (RIGR) method used leads to ill-conditioned linear systems with Hermitian Toeplitz matrix and noisy right-hand side. We analyze the behavior of some regularization methods such as the truncated singular value decomposition (TSVD), the Lavrent'yev regularization method and conjugate gradients (CG) type iterative methods. For what concerns the choice of the regularization parameter, we use some known methods and we propose new heuristic criteria for iterative regularization methods. The simulations are carried on test problems obtained from real data acquired on a 1.5 T Phillips system.

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