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A Lorentzian-Function-Sparsity Approach for Fast High-Dimensional Magnetic Resonance Spectroscopy

B Jiang

B Jiang1*, X Hu2 , H Gao3 , (1) Shanghai Jiao Tong University, Shanghai, Shanghai(2) Emory University and Georgia Institute of Technology, Atlanta, GA, (3) Shanghai Jiao Tong University, Shanghai, Shanghai


SU-D-303-7 (Sunday, July 12, 2015) 2:05 PM - 3:00 PM Room: 303

Purpose: High-dimensional magnetic resonance spectroscopy (MRS) is challenging, even with the state-of-art L1-sparsity based compressive reconstruction method. For example, the reconstructed spectroscopy quality deteriorates dramatically with 25% undersampled 2D MRS data. In this work, using the prior that the MRS consists of Lorentzian functions, we aim to develop a robust Lorentzian-function-sparsity based spectroscopy reconstruction method for high-dimensional MRS.

Methods: The proposed method utilizes the sparsity via Lorentzian functions. That is, instead of reconstructing thousands of pixel-wise unknowns, the Lorentzian-function based approaches considers the parameter reconstruction with only tens of unknowns, i.e., the center, magnitude and the shape for each Lorentzian function. And the simulated annealing algorithm is developed to find a global minimizer for this small-scale nonlinear and nonconvex optimization problem, in which the 1D Fourier transform of the first k-line is used to identify the initial guesses of centers and magnitudes.

Results: The proof-of-concept simulations were performed for 2D MRS. First we compared FFT method, L1-sparsity method and Lorentzian-function-sparsity method with 25% undersampled data for a simple single-peak case, during which FFT and L1 results contained severe artifacts while the Lorentzian method was able to provide nearly perfect reconstructed image. Then we tested a more practical case with seven peaks of widely ranged peak intensities, during which Lorentzian method was still able to provide almost perfect reconstruction result even with 1% undersampled data.

Conclusion: A new MRS reconstruction method is proposed using the Lorentzian-function-based sparsity, with significantly reduced number of unknown variables. The new method can achieve significantly better MRS reconstruction results than FFT method or L1-based sparsity method, e.g., even with 1% k-space data.

Funding Support, Disclosures, and Conflict of Interest: Boyu Jiang and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500).

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