vSHARP: Variable Splitting Half-quadratic ADMM algorithm for reconstruction of inverse-problems

• Published in: Magnetic resonance imaging Vol. 115; p. 110266
• Main Authors: Yiasemis, George, Moriakov, Nikita, Sonke, Jan-Jakob, Teuwen, Jonas
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier Inc 01.01.2025
• Subjects: Algorithms; Alternating direction method of multipliers; Brain - diagnostic imaging; Deep Learning; Deep MRI reconstruction; Half-quadratic variable splitting; Humans; Image Processing, Computer-Assisted - methods; Inverse problems; Magnetic Resonance Imaging - methods; Mathematical optimization; Medical imaging reconstruction; Phantoms, Imaging; Signal-To-Noise Ratio; Alternating direction method of multipliers; Inverse problems; Deep MRI reconstruction; Medical imaging reconstruction; Mathematical optimization; Half-quadratic variable splitting
• ISSN: 0730-725X; 1873-5894; 1873-5894
• DOI: 10.1016/j.mri.2024.110266

Medical Imaging (MI) tasks, such as accelerated parallel Magnetic Resonance Imaging (MRI), often involve reconstructing an image from noisy or incomplete measurements. This amounts to solving ill-posed inverse problems, where a satisfactory closed-form analytical solution is not available. Traditional methods such as Compressed Sensing (CS) in MRI reconstruction can be time-consuming or prone to obtaining low-fidelity images. Recently, a plethora of Deep Learning (DL) approaches have demonstrated superior performance in inverse-problem solving, surpassing conventional methods. In this study, we propose vSHARP (variable Splitting Half-quadratic ADMM algorithm for Reconstruction of inverse Problems), a novel DL-based method for solving ill-posed inverse problems arising in MI. vSHARP utilizes the Half-Quadratic Variable Splitting method and employs the Alternating Direction Method of Multipliers (ADMM) to unroll the optimization process. For data consistency, vSHARP unrolls a differentiable gradient descent process in the image domain, while a DL-based denoiser, such as a U-Net architecture, is applied to enhance image quality. vSHARP also employs a dilated-convolution DL-based model to predict the Lagrange multipliers for the ADMM initialization. We evaluate vSHARP on tasks of accelerated parallel MRI Reconstruction using two distinct datasets and on accelerated parallel dynamic MRI Reconstruction using another dataset. Our comparative analysis with state-of-the-art methods demonstrates the superior performance of vSHARP in these applications. [Display omitted] •vSHARP is a new deep learning method that combines Half-Quadratic Variable Splitting with ADMM for solving inverse problems in medical imaging, enhancing image quality effectively.•Each vSHARP iteration consists of a three-step ADMM-based process: a DL-based denoiser refines the auxiliary variable, a differentiable gradient descent ensures data consistency for the image, and an update of Lagrange multipliers.•vSHARP outperforms state-of-the-art methods in accelerated static and dynamic MRI reconstruction, achieving better SSIM, pSNR, and NMSE metrics on brain, prostate and cardiac datasets.