Research On Deep Learning Reconstruction Method Of Compressive Sensing Magnetic Resonance Imaging

The inverse problem is a new interdisciplinary field that originates from practical problems in many scientific fields and is generated through mathematical modeling.In the past two decades,due to the urgent needs of other disciplines and practical applications.inverse problems have become one of the fastest growing fields in applied mathematics.So far.it has become a popular discipline in interdisciplinary computational mathematics,applied mathematics,and systems science,and has important applications in various industries,such as the related parameter inversion problems based on the pricing BlackScholes model in financial mathematics,scanning imaging,and so on.As an inverse problem,reconstruct the Magnetic resonance imaging(MRI)from undersampled measurements is ill-posedness.But MRI has the unique advantages of no ionizing radiation,no need of radioactive tracer,high soft tissue contrast,etc while compared with other imaging modes(such as ultrasound,CT.PET.etc.).As a non-invasive imaging method,magnetic resonance imaging(MRI)has the characteristics of safety and high imaging quality,which provides rich information for clinical diagnosis and has become one of the important means of clinical medical examination.However,the long scanning time and slow imaging speed seriously hinder the promotion and use of MRI.Due to the limitation of Nyquist-Shannon sampling frequency,the traditional magnetic resonance accelerated sampling methods have limited improvement on the magnetic resonance scanning speed.Therefore,achieving rapid MRI imaging has great clinical and economic value,and has also become a hot and difficult issue in the field of MRI research.Compressive sensing(CS).which can recover signals from undersampled samples that violate the Nyquist-Shannon sampling theorem,provides a new direction for accelerating MRI.Its sampling rate can be much lower than the Nyquist rate.In recent years,compressive sensing theory has been widely used in the field of MRI,and some algorithms have been proposed to improve imaging quality and reduce imaging time.However,the existing algorithms have shortcomings such as high complexity and slow convergence speed.Besides,some algorithms have strict requirements,which also limit the use of them.In addition,the existed algorithms are not satisfactory in image boundary process.In this paper,we treat the CS-MRI image reconstruction problem as an inverse problem and try to solve it with deep learning.we treat the PM model.which is originally used to process the image boundary,as a regularization term and introduce it into the CS image reconstruction model.We get two versions of the reconstruction model after two versions of the sparsity constraint be introduced into CS model.and then we get two versions of solver.After that,we unroll them into deep neural networks.Instead of setting the transform mapping and hyperparam eters of the solver manually,we learn them uncertainties during training.NRD-CSNets naturally inherit the knowledge from imaging mechanism and internal relationship of measurement-label pair.Our NRD-CSNets is a new deep architecture for solving CS imaging models with regularization terms.CS imaging numerical experiments show that NRD-CSNets can achieve outperform or comparable perfor mance in favorable imaging speed,especially at lower sampling rates.In addition,compared with the existing methods,XRD-CSNets has better stability in terms of noise impact,and has significant improvement in structural similarity(SSIM)and peak signal-to-noise ratio(PSNR).Besides.our methods has the best results for boundary process.