Fast Two-dimensional Magnetic Spectroscopy Reconstruction Based On Lorentzian Sparsity

Reconstruction for two-dimensional magnetic spectroscopy(2D MRS)is challenging.Compressed sensing-based reconstruction is a popular trend in magnetic resonance reconstruction issue.However,they may fail under high undersampling rate.This thesis has proposed a parameterized reconstruction method,where Lorentzian function is utilized to represent absorption peaks in 2D MRS.Traditional pixel-wised methods will face the problem with over thousands of unknowns,while parameter-based method just need to deal with tens or hundreds of unknowns.These parameters are centers,scale and shape of each peak.Objective function here is non-convex and non-linear,which will be solved by simulated annealing method.Results of Lorentzian sparsity-based method show higher quality than traditional FFT and Compressed Sensing method under different undersampling rate.In addition,reconstruction of multi-case works as well.With addition of different levels of noise,the proposed method still holds its robustness.