Null Space Matters: Range-Null Decomposition for Consistent Multi-Contrast MRI Reconstruction

Consistency and interpretability have long been the critical issues in MRI reconstruction. While interpretability has been dramatically improved with the employment of deep unfolding networks (DUNs), current methods still suffer from inconsistencies and generate inferior anatomical structure. Especially in multi-contrast scenes, different imaging protocols often exacerbate the concerned issue. In this paper, we propose a range-null decomposition-assisted DUN architecture to ensure consistency while still providing desirable interpretability. Given the input decomposed, we argue that the inconsistency could be analytically relieved by feeding solely the null-space component into proximal mapping, while leaving the range-space counterpart fixed. More importantly, a correlation decoupling scheme is further proposed to narrow the information gap for multi-contrast fusion, which dynamically borrows isotropic features from the opponent while maintaining the modality-specific ones. Specifically, the two features are attached to different frequencies and learned individually by the newly designed isotropy encoder and anisotropy encoder. The former strives for the contrast-shared information, while the latter serves to capture the contrast-specific features. The quantitative and qualitative results show that our proposal outperforms most cutting-edge methods by a large margin. Codes will be released on https://github.com/chenjiachengzzz/RNU.