磁気共鳴画像法におけるTV正則化のためのNesterov加速スペクトル共役勾配法

Magnetic Resonance Imaging (MRI) as a representative of noninvasive medical imaging, it has excellent soft tissue resolution, multi-parameter imaging capability and no radiation, thus it has been widely used in the fields of disease diagnosis, treatment and drug development. However, MRI technology still has problems such as long time consuming, sensitive to motion artefacts, and difficult to balance the imaging effect and speed. In this paper, a Nesterov accelerated spectral conjugate gradient algorithm (TV_NASCG) for MRI with TV regularisation is established from optimising reconstruction algorithms based on Total Variation (TV) regularised MRI model. The algorithm is based on a set of conjugate and spectral parameters proposed in this paper, and inspired by Nesterov acceleration technique, a set of Nesterov acceleration extrapolation step and acceleration parameter are proposed. In this paper, we also use step size acceleration technique and Powell restart strategy to further improve performance of the algorithm. In addition, we give a convergence analysis of TV_NASCG algorithm, which proves that it is sufficiently descent and globally convergent. Finally, in order to verify MRI performance of TV_NASCG algorithm, it was tested in MRI experiment and compared with other algorithms, and experimental results show that TV_NASCG algorithm can improve MRI quality and shorten imaging time.