Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI Reconstruction
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914102001008640 |
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| author | Hong, Tao Xu, Zhaoyi Chun, Se Young Hernandez-Garcia, Luis Fessler, Jeffrey A. |
| author_facet | Hong, Tao Xu, Zhaoyi Chun, Se Young Hernandez-Garcia, Luis Fessler, Jeffrey A. |
| contents | In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two general frameworks that use denoisers as the prior. While PnP/RED methods with convolutional neural networks (CNNs) based denoisers outperform classical hand-crafted priors in CS MRI, their convergence theory relies on assumptions that do not hold for practical CNNs. The recently developed gradient-driven denoisers offer a framework that bridges the gap between practical performance and theoretical guarantees. However, the numerical solvers for the associated minimization problem remain slow for CS MRI reconstruction. This paper proposes a complex quasi-Newton proximal method that achieves faster convergence than existing approaches. To address the complex domain in CS MRI, we propose a modified Hessian estimation method that guarantees Hermitian positive definiteness. Furthermore, we provide a rigorous convergence analysis of the proposed method for nonconvex settings. Numerical experiments on both Cartesian and non-Cartesian sampling trajectories demonstrate the effectiveness and efficiency of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI Reconstruction Hong, Tao Xu, Zhaoyi Chun, Se Young Hernandez-Garcia, Luis Fessler, Jeffrey A. Image and Video Processing Numerical Analysis Optimization and Control In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two general frameworks that use denoisers as the prior. While PnP/RED methods with convolutional neural networks (CNNs) based denoisers outperform classical hand-crafted priors in CS MRI, their convergence theory relies on assumptions that do not hold for practical CNNs. The recently developed gradient-driven denoisers offer a framework that bridges the gap between practical performance and theoretical guarantees. However, the numerical solvers for the associated minimization problem remain slow for CS MRI reconstruction. This paper proposes a complex quasi-Newton proximal method that achieves faster convergence than existing approaches. To address the complex domain in CS MRI, we propose a modified Hessian estimation method that guarantees Hermitian positive definiteness. Furthermore, we provide a rigorous convergence analysis of the proposed method for nonconvex settings. Numerical experiments on both Cartesian and non-Cartesian sampling trajectories demonstrate the effectiveness and efficiency of our approach. |
| title | Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI Reconstruction |
| topic | Image and Video Processing Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2505.04820 |