Generalized Nesterov Accelerated Conjugate Gradient Algorithm for a Compressively Sampled MR Imaging Reconstruction

To accelerate the scanning speed of magnetic resonance imaging (MRI) and improve the quality of magnetic resonance (MR) image reconstruction, a fast MRI technology based on compressed sensing is proposed. Nesterov's accelerated gradient descent (NAG) algorithm uses Nesterov acceleration to optimize the gradient descent (GD) method. However, this form of acceleration factor uses a fixed iteration curve update and can not adapt to different iteration processes. A generalized Nesterov acceleration concept is proposed. Combining the total variation model, a generalized Nesterov accelerated conjugate gradient based on total variation (GNACG_TV) algorithm is proposed. It extends the acceleration factor in a generalized manner, introducing the Frobenius norm of the objective function as a parameter, so that the acceleration factor is related not only to the number of iterations but also to the iteration process and guarantees the convergence of the iterative process. Experiments on three MR images (abdomen, head, and ankles) at different sampling ratios show that the proposed GNACG_TV algorithm compares favorably with conjugate gradient (CG), conjugate gradient based on total variation (CG_TV), Nesterov accelerated conjugate gradient based on total variation (NACG_TV), and conjugate gradient based on adaptive moment estimation (ADAMCG) algorithms in the MSE, PSNR and SSIM exhibit better performance and robustness in denoising performance for the proposed algorithm. Comparing with the result of qualitative and quantitative analysis, it was concluded that the proposed method can better reconstruct under-sampled MR images than other 4 methods. GNACG_TV can further improve the convergence speed based on Nesterov acceleration and get better reconstruction performance.