Recovery Of Magnetic Resonance Spectra Based On Low-Rank Block Hankel Matrix

Magnetic resonance spectroscopy(MRS)serves as a indispensable tool for protein structure analysis and material composition analysis in biomedical engineering.Multidi-mensional MRS resolves spectral peak overlap and provides new information about the re-lationship between atomic nuclei,which is of great significance for the analysis of complex biological macromolecules.However,limited by physical mechanisms such as evolution time of indirect dimension,the data acquisition time of typical multidimensional spectrum increases sharply with the rise of dimensionality and resolution.Therefore,accelerating the acquisition process of multidimensional MRS is of great importance.Having been one of typical approaches for speeding up data acquisition,the spatio-temporally encoded technology seeks to optimize experimental pulse sequences.Fast data acquisition is achieved by coding the frequency information in direct dimension concur-rently,but the technique requires strong data acquisition gradient that may causes dam-ages to the instrument.To alleviate the demand of strong pulse gradient,the non-uniform sampling is introduced into the spatio-temporally encoded MRS.However,this operation results in data points missing in the hybrid time and frequency plane.From the perspective of signal processing,how to perform high-quality reconstruc-tion of the hybrid time and frequency signal possesses as a challenging problem.The most cutting-edge method is to recover the spatio-temporally encoded data by enforcing the sparsity of the spectrum.However,this approach may cause distortion and even loss of spectral peaks.Therefore,it is urgent to build new signal reconstruction methods.In this thesis,starting from the low-rank characteristics of time-domain MRS signals,we exploit how to model hybrid time and frequency signal into exponential functions to recover missing data points.The work includes:(a)Propose a hybrid time and frequency signal reconstruction approach based on low-rank block Hankel matrix,and deduce its fast numerical algorithm.Experimental results show that spectral peaks reconstructed by the proposed method is more consistent to the fully sampled spectral peaks than that by spectrum sparse based method,and achieves more accurately quantification of the pro-ton resonance volume in the material enjoying more than 5 times quantification accuracy,(b)By introducing the approximation function of matrix rank,we propose a low-rank signal approximation reconstruction model based on block Hankel matrix,and its nu-merical algorithm is deduced.Both experimental results on synthetic and acquired 2D spatio-temporally encoded MRS show that only 10%of the data is required by proposed approach to obtain the comparable peak intensity correlation results that produced by the first proposed method with 20%data,and about 1～4 times improvement of quantification accuracy of proton resonance volume is achieved.Proposed methods may be extended to other MRS reconstruction problem such as MRS denoising and the reconstruction of other 2D exponential signals.Proposed methods can be further explored in algorithm convergence and large-scale low-rank reconstruction algorithms.