Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction

IF 4.2 2区 计算机科学 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC IEEE Transactions on Computational Imaging Pub Date : 2024-10-09 DOI:10.1109/TCI.2024.3477329
Tao Hong;Xiaojian Xu;Jason Hu;Jeffrey A. Fessler
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Abstract

Model-based methods play a key role in the reconstruction of compressed sensing (CS) MRI. Finding an effective prior to describe the statistical distribution of the image family of interest is crucial for model-based methods. Plug-and-play (PnP) is a general framework that uses denoising algorithms as the prior or regularizer. Recent work showed that PnP methods with denoisers based on pretrained convolutional neural networks outperform other classical regularizers in CS MRI reconstruction. However, the numerical solvers for PnP can be slow for CS MRI reconstruction. This paper proposes a preconditioned PnP ( $\text{P}^{2}$ nP) method to accelerate the convergence speed. Moreover, we provide proofs of the fixed-point convergence of the $\text{P}^{2}$ nP iterates. Numerical experiments on CS MRI reconstruction with non-Cartesian sampling trajectories illustrate the effectiveness and efficiency of the $\text{P}^{2}$ nP approach.
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压缩传感磁共振成像重建的可证明预处理即插即用方法
基于模型的方法在压缩传感(CS)磁共振成像重建中发挥着关键作用。找到一个有效的先验来描述感兴趣图像族的统计分布对于基于模型的方法至关重要。即插即用(PnP)是一种使用去噪算法作为先验或正则的通用框架。最近的研究表明,在 CS MRI 重建中,基于预训练卷积神经网络的去噪器的即插即用方法优于其他经典正则。然而,PnP 的数值求解器在 CS MRI 重建中速度较慢。本文提出了一种预条件 PnP($\text{P}^{2}$nP)方法来加快收敛速度。此外,我们还证明了 $\text{P}^{2}$nP 迭代的定点收敛性。在 CS MRI 重建中使用非笛卡尔采样轨迹的数值实验说明了 $\text{P}^{2}$nP 方法的有效性和效率。
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来源期刊
IEEE Transactions on Computational Imaging
IEEE Transactions on Computational Imaging Mathematics-Computational Mathematics
CiteScore
8.20
自引率
7.40%
发文量
59
期刊介绍: The IEEE Transactions on Computational Imaging will publish articles where computation plays an integral role in the image formation process. Papers will cover all areas of computational imaging ranging from fundamental theoretical methods to the latest innovative computational imaging system designs. Topics of interest will include advanced algorithms and mathematical techniques, model-based data inversion, methods for image and signal recovery from sparse and incomplete data, techniques for non-traditional sensing of image data, methods for dynamic information acquisition and extraction from imaging sensors, software and hardware for efficient computation in imaging systems, and highly novel imaging system design.
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