CSSL-ISRVN: consistency self-supervised learning integrating ISTANet and sensitivity refinement-enhanced variational network for accelerated MRI reconstruction

<i>Objective</i>. Magnetic resonance imaging is essential in clinical practice due to its non-invasive nature and superior soft-tissue contrast. However, long acquisition times remain a major limitation, leading to motion artifacts and patient discomfort. Most deep learning approaches rely on fully sampled datasets, which are often difficult to obtain. This study aims to develop a self-supervised framework for MRI reconstruction that eliminates dependence on fully sampled training data.<i>Approach</i>. We propose consistency self-supervised learning with ISRVN (CSSL-ISRVN), a novel consistency self-supervised reconstruction framework. At its core lies SRVN, which combines an improved variational network (IVN) with a sensitivity refinement module (SRM). The IVN integrates a feature refinement and denoising module (FRDM), composed of residual blocks (RB) and a Gaussian context transformer (GCT), to jointly extract local and global features. Meanwhile, SRM iteratively refines a task-driven implicit sensitivity modulation variable using the previously reconstructed full<i>k</i>-space in a reconstruction-sensitivity closed loop, adaptively modulating the multi-coil forward model and data consistency to reduce error accumulation induced by fixed auto-calibration signals-based sensitivity estimates under undersampling. Building on ISTANet and SRVN, we develop ISRVN, a heterogeneous alternating cascade of ISTANet and SRVN: ISTANet first suppresses undersampling artifacts in the multi-coil complex domain to provide cleaner intermediates, enabling SRVN to perform encoding-modulated, physics-consistent refinement for improved reconstruction quality and stability. To eliminate dependence on fully sampled data, we introduce a consistency self-supervised scheme that re-undersamples the original<i>k</i>-space to train two pairs of consistency networks using calibration and consistency losses.<i>Results</i>. Experiments on three public datasets show that CSSL-ISRVN consistently surpasses existing self-supervised and scan-specific methods, particularly under 1D undersampling masks. It achieves performance competitive with state-of-the-art supervised models.<i>Significance</i>. CSSL-ISRVN offers an effective solution for accelerated MRI reconstruction without fully sampled labels. Its integration of sensitivity refinement, hybrid modeling, and consistency self-supervision enables robust, high-fidelity reconstructions, underscoring its potential for real-world clinical deployment.