燕山大学学报2024，Vol.48Issue(3)：244-254,11.DOI:10.3969/j.issn.1007-791X.2024.03.007
基于可显式证明梯度网络的压缩感知磁共振成像算法研究
Compressive sensing magnetic resonance imaging algorithms based on explicitly provable gradient networks
摘要
Abstract
Compressive sensing magnetic resonance imaging(CSMRI)aims to reconstruct the original magnetic resonance image using under-sampled k-space data.In recent years,the unrolled algorithm attracts significant attention from scholars in the field of CSMRI image reconstruction.However,current unrolled algorithms still face the challenge of achieving high-quality reconstructions.Moreover,due to the intricate structure of prior networks,the designed prior network often lacks model architecture interpretability,making it challenging to demonstrate that the prior network satisfies the convergence conditions of the unrolled algorithm,such as the Lipschitz condition.To address these issues,this paper introduces an explicitly provable gradient network,demonstrates its satisfaction of the Lipschitz condition,and analyzes the convergence of the unrolled algorithm based on this gradient network.Furthermore,a regularization model based on the gradient network is proposed,and an associated reconstruction optimization model is formulated based on this model,which is solved using the alternating optimization approach.Lastly,the unrolled algorithm is constructed as a deep unrolled network.Simulation results show that compared to DLMRI,NLR,BM3D-MRI,BM3D-AMP,ADMM-CSNet,and IDPCNN algorithms,the deep unrolled network exhibits an average peak signal-to-noise ratio improvement of 2.62 dB,1.59 dB,1.61 dB,2.05 dB,0.51 dB,and 0.53 dB across various sampling rates.Furthermore,the knee joint images reconstructed by the deep unrolled network effectively preserve image details and achieve good visual outcomes,thus validating the efficacy of the constructed deep unrolled network.关键词
压缩感知磁共振成像/梯度网络/深度展开网络/收敛性分析Key words
compressive sensing magnetic resonance imaging/gradient network/deep unrolled network/convergence analysis分类
信息技术与安全科学引用本文复制引用
李凌雁,徐文媛,刘政,石保顺,王芳..基于可显式证明梯度网络的压缩感知磁共振成像算法研究[J].燕山大学学报,2024,48(3):244-254,11.基金项目
国家自然科学基金资助项目(62371414) （62371414）
河北省自然科学基金资助项目(F2023203043,D2020203007,F2020203025) （F2023203043,D2020203007,F2020203025）
河北省教育厅科学研究项目(SQ2023109) （SQ2023109）
教育部人文社会科学基金资助项目(18YJC790084). （18YJC790084）
