Dense recurrent neural networks for accelerated mri: History-cognizant unrolling of optimization algorithms

Seyed Amir Hossein Hosseini, Burhaneddin Yaman, Steen Moeller, Mingyi Hong, Mehmet Akcakaya

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40 Scopus citations


Inverse problems for accelerated MRI typically incorporate domain-specific knowledge about the forward encoding operator in a regularized reconstruction framework. Recently physics-driven deep learning (DL) methods have been proposed to use neural networks for data-driven regularization. These methods unroll iterative optimization algorithms to solve the inverse problem objective function, by alternating between domain-specific data consistency and data-driven regularization via neural networks. The whole unrolled network is then trained end-To-end to learn the parameters of the network. Due to simplicity of data consistency updates with gradient descent steps, proximal gradient descent (PGD) is a common approach to unroll physics-driven DL reconstruction methods. However, PGD methods have slow convergence rates, necessitating a higher number of unrolled iterations, leading to memory issues in training and slower reconstruction times in testing. Inspired by efficient variants of PGD methods that use a history of the previous iterates, in this article, we propose a history-cognizant unrolling of the optimization algorithm with dense connections across iterations for improved performance. In our approach, the gradient descent steps are calculated at a trainable combination of the outputs of all the previous regularization units. We also apply this idea to unrolling variable splitting methods with quadratic relaxation. Our results in reconstruction of the fastMRI knee dataset show that the proposed history-cognizant approach reduces residual aliasing artifacts compared to its conventional unrolled counterpart without requiring extra computational power or increasing reconstruction time.

Original languageEnglish (US)
Article number9119770
Pages (from-to)1280-1291
Number of pages12
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number6
StatePublished - Oct 2020

Bibliographical note

Funding Information:
Manuscript received December 15, 2019; revised April 27, 2020 and June 4, 2020; accepted June 5, 2020. Date of publication June 17, 2020; date of current version September 24, 2020. This work was supported in part by NIH under Grant P41EB027061 and Grant U01EB025144, in part by NSF CAREER under Grant CCF-1651825, in part by NSF under Grants CMMI-1727757 and CIF-1910385, and in part by ARO under Grant 73202-CS. The guest editor coordinating the review of this manuscript and approving it for publication was Vishal Monga. (Corresponding author: Mehmet Akçakaya.) Seyed Amir Hossein Hosseini, Burhaneddin Yaman, and Mehmet Akçakaya are with the Department of Electrical and Computer Engineering, and Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:;;

Publisher Copyright:
© 2007-2012 IEEE.


  • Inverse problems
  • MRI reconstruction
  • neural networks
  • physics-driven deep learning
  • recurrent neural networks
  • unrolled optimization algorithms


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