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Medical Imaging (MI) tasks, such as accelerated Parallel Magnetic ResonanceImaging (MRI), often involve reconstructing an image from noisy or incompletemeasurements. This amounts to solving ill-posed inverse problems, where asatisfactory closed-form analytical solution is not available. Traditionalmethods such as Compressed Sensing (CS) in MRI reconstruction can betime-consuming or prone to obtaining low-fidelity images. Recently, a plethoraof supervised and self-supervised Deep Learning (DL) approaches havedemonstrated superior performance in inverse-problem solving, surpassingconventional methods. In this study, we propose vSHARP (variable SplittingHalf-quadratic ADMM algorithm for Reconstruction of inverse Problems), a novelDL-based method for solving ill-posed inverse problems arising in MI. vSHARPutilizes the Half-Quadratic Variable Splitting method and employs theAlternating Direction Method of Multipliers (ADMM) to unroll the optimizationprocess. For data consistency, vSHARP unrolls a differentiable gradient descentprocess in the image domain, while a DL-based denoiser, such as a U-Netarchitecture, is applied to enhance image quality. vSHARP also employs adilated-convolution DL-based model to predict the Lagrange multipliers for theADMM initialization. We evaluate the proposed model by applying it to the taskof accelerated Parallel MRI Reconstruction on two distinct datasets. We presenta comparative analysis of our experimental results with state-of-the-artapproaches, highlighting the superior performance of vSHARP.

vSHARP: variable Splitting Half-quadratic ADMM algorithm for Reconstruction of inverse-Problems