| Magnetic resonance spectroscopy(MRS)serves as one of the important means to analyze the chemical components and study the molecular structure,and has been widely used in many fields,such as chemistry,biology and medicine.Molecular self-diffusion reflects the mobility of molecules.Diffusion-ordered NMR spectroscopy(DOSY)can non-invasively separate mixture by combining the diffusion dimension and the frequency dimension,according to different diffusion coefficients of different molecules,without destroying the structure of the original mixture.At the same time,in order to improve the resolution of the spectrum and reduce the overlap of spectral peaks,researchers combine the diffusion dimension with traditional two-dimensional spectroscopy to form a three-dimensional diffusion spectroscopy.However,the sampling time of high-dimensional spectroscopy increases exponentially with the increase of dimension,which hinders the application of high-dimensional spectrum.A typical method to reduce the sampling time is to acquire part of the magneticresonance signal in the indirect dimension.For example,for the high-dimensional diffusion spectroscopy,the two dimensions of the indirect dimension plane are the time dimension and the exponential decay dimension.The time dimension signal is a sum of first-order complex exponential signals,which can be inverted by the Fourier transform to the spectrum,and the exponential decay dimension signal is generated by diffusion gradient and can be modeled as a sum of second-order exponential signals that can be inverted by a Laplace inverse transform to the distribution of the diffusion coefficients.Undersampling in this plane will result in simultaneous loss of signals in both dimensions,which poses a challenge for signal reconstruction.The most cutting-edge method is to reconstruct the diffusion spectroscopy by constraining the sparsity of the diffusion spectroscopy plane.However,each point in the spectroscopy is isolated in the sparse constraint reconstruction process and does not make use of the properties of the diffusion spectroscopy itself,that is,the diffusion coefficients of the same substance are the same,and the diffusion coefficients of different substances are different,which easily causes the reconstruction spectrum and the diffusion coefficient error.Therefore.it is necessary to develop a high-fidelity diffusion spectroscopy reconstruction method,which is also the research content of this paper.The main research work of this paper includes:(1)Using the property that the diffusion coefficient of the same substance is the same and assuming that the inverse diffusion spectrum has low rank characteristics,propose a diffusion spectroscopy undersampling reconstruction model based on spectroscopy plane low rank and sparsity,and design its numerical algorithm.The experimental results show that the proposed method can reconstruct the diffusion spectroscopy with more accurate diffusion coefficient,fewer pseudo peaks and noise,and the diffusion coefficient has better consistency.(2)Propose a hybrid time and exponential decay signal recovery method based on low rank Hankel matrix,and design an alternating direction solving algorithm.The method constrains the low rank of one-dimensional time domain signal to Hankel matrix and the sparsity of the inverse Laplace transform of exponentially decaying in the iterative process.The experimental results show that the error between the hybrid signal recovered by the proposed method and the fully sampled signal is smaller,and the peak intensity is higher.Proposed methods take the diffusion spectroscopy as an application example,but these methods can also be promoted to other magnetic resonance spectroscopy whose sampling signals are also modeled as hybrid time and exponential decay signal,such as hybrid time and relaxation delay dimensions MRS signal.In addition,the proposed method can be further optimized in computation time and reconstruction models that are more in line with physical characteristics. |
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