Parallel Magnetic Resonance Imaging Reconstruction Based On Deep Energy-Based Learning

Magnetic Resonance Imaging(MRI)is to generate images of internal physical and chemical characteristics of objects through externally measured MR signals,which is mainly applied in the medical field.Compared with other imaging modalities,MRI,as a non-invasive examination method,has no ionizing radiation damage,can be used for multi-directional and multi-sequence imaging.MRI has good soft tissue imaging,no radiation,high specificity and sensitivity for musculoskeletal diseases,and high imaging resolution for muscle and soft tissue.However,the main disadvantages of MRI are the long data acquisition time and the confinement of the patient to a relatively closed space.Therefore,accelerated magnetic resonance imaging is the key research direction of current medical imaging,which is related to the broadening of its application fields and the improvement of patient experience.Recent researches have demonstrated that deep generative models have great potential in accelerating magnetic resonance image acquisition and reconstruction.But tailored methods to ensure high-quality reconstructions are still lacking.In this work,deep energy-based models(EBMs)are studied and used for accelerated parallel MRI(p MRI)reconstruction.Deep energy-based models are very flexible in terms of distribution parameterization.To further advance the study of generative models,the energy-based model is trained in a way that minimizes the f-divergence,enabling the energy-based model to be trained using any f-divergence.Using the dual form,alternating minimization methods are employed in both prior learning and iterative reconstruction.The optimization algorithm can train a deep energy-based model of any f-divergence,construct the prior information of p MRI through the deep energy-based model based on the minimization of f-divergence,and incorporate it into the iterative minimization process for p MRI reconstruction.The main contributions of this work are as follows:(1)Applying a deep energy-based model to parallel magnetic resonance reconstruction.Deep energy-based models are very flexible in distribution parameterization,but computationally challenging due to the intractability of the partition function.In this paper,the dual form is adopted to avoid the computation of the partition function.In addition,other f-divergences show advantages in training implicit density generative models,based on the properties of f-divergence,combining f-divergence minimization with an energy-based model and its application in parallel magnetic resonance reconstruction is comprehensively studied.Alternate minimization methods are employed in prior learning and iterative reconstruction,using Langevin dynamics for efficient sampling via gradient information.(2)The phenomenon that this method is applied to complex-valued parallel magnetic resonance imaging is consistent with that of real-valued natural image generation: Jensen-Shannon divergence and Squared Hellinger divergence have better effects.It shows that the imaging reconstruction task is similar to the image generation task in essence,and the prior information of the energy-based model does play a good role in the parallel magnetic resonance reconstruction.The experimental results under different conditions show that the proposed algorithm is superior to the state-of-the-art algorithms in various evaluation indicators,and can effectively improve the reconstruction quality.The density ratio estimation and iterative optimization trajectory prove that the f EBM model can recover the real data distribution.