并行压缩感知磁共振成像(parallel compressive sensing magnetic resonance imaging,p-CSMRI)算法旨在利用多线圈采样的部分k域数据重建原始图像.近些年基于学习的模型驱动p-CSMRI算法以较高的重建质量受到了广泛的关注,然而其先验网络架构通常基于经验设计,缺乏模型可解释性,导致算法收敛性难以分析.因此,该文构建了可证明有界的深度去噪器,并将其作为先验模块融合到模型驱动的p-CSMRI网络中,提出了收敛性可分析的深度展开p-CSMRI算法.首先基于对偶标架结合设计的深度阈值网络,构建了满足有界条件的深度去噪器;其次构建了基于对偶标架的p-CSMRI优化模型,并将对应的迭代步骤展开成了一个可端到端有监督训练的深度神经网络;最后利用可证明有界的先验模块提出 了可分析收敛性的算法框架.仿真实验表明,在4倍加速因子下,通过所提算法重建图像的峰值信噪比相较Modl、VN和VS-Net算法分别提高了 1.70、1.45和0.46dB.该文从理论层面证明了构建的深度去噪器满足有界条件,并分析了所提算法的收敛性.
Model-driven parallel compressive sensing magnetic resonance imaging algorithm based on trainable dual frames and its convergence analysis
[Objective]Parallel compressive sensing magnetic resonance imaging(p-CSMRI)algorithms aim to improve and refine the reconstructed image using partial k-space data sampled from multiple coils.Recently,learning-based model-driven p-CSMRI algorithms have attracted extensive attention because of their superior reconstruction quality.Nevertheless,their prior network architectures are typically designed empirically,lacking model interpretability and hampering the analysis of algorithm convergence.To address this problem,we introduce a provably bounded denoiser based on deep learning and incorporate it as a prior module into a model-driven p-CSMRI network.Moreover,we propose a deep unrolled p-CSMRI algorithm;its convergence can be explicitly analyzed.[Methods]First,to improve the sparse representation capability and learning speed of traditional tight frames,we extend the single tight frame to a dual-frame network.Because the image pixels vary in the spatial domain,a deep threshold network is developed to adaptively extract thresholds from the input images,thereby improving the generalization ability of the dual frames.Based on the dual frames integrated with the elaborated deep threshold network,we introduce a novel provably bounded deep denoiser.Second,we describe a p-CSMRI optimization model based on dual frames.The constructed optimization model is iteratively solved via the half-quadratic splitting solver,and the corresponding iterations are unfolded into a deep neural network that can be trained by end-to-end supervised learning.Finally,under reducing noise level conditions,the convergence of model-driven p-CSMRI algorithms is explicitly proved based on the bounded denoiser theory.The convergence theory of plug-and-play(PnP)imaging methods demonstrates that methods with decreasing noise levels can realize a fixed-point convergence under the assumption of a bounded denoiser.We explicitly prove that the proposed deep denoiser as the prior network is bounded.Based on this bounded property,we develop a model-driven p-CSMRI algorithmic framework with guaranteed convergence.[Results]Theoretically,we explicitly prove that the built deep denoiser as the prior network satisfies the bounded property and perform a convergence analysis of the proposed algorithm under the mild condition of gradually decreasing noise.Simulation experiments carried out on the knee MRI dataset from New York University disclose that,compared with the Modl,VN,and VS-Net algorithms,the proposed method realizes improvements of 1.70,1.45,and 0.46 dB,respectively,in peak signal-to-noise ratio for reconstructed images under a fourfold acceleration factor.However,a comparative assessment of the proposed model with Modl,VN,and VS-Net algorithms concerning parameter memory and average inference time reveals that the model-driven p-CSMRI method based on the dual frames recommended in this study has a high number of parameters.Furthermore,the image inference time of the proposed method is lower than those of Modl and VN and slightly higher than that of VS-Net.Therefore,our proposed method shows a moderate level of computational complexity.[Conclusions]The model-driven p-CSMRI network algorithm proposed here,based on trainable dual frames,has a theoretical convergence guarantee and demonstrates stable performance in experiments.Moreover,our algorithm proved effective in reconstructing high-quality MR images.This work offers valuable insights into future research and development in the area of magnetic resonance imaging.
compressive sensing magnetic resonance imagingparallel imagingdual framesconvergence analysisdeep unrolled network
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维普
