  Medical imaging tasks often involve multiple contrasts, such as T1- and
T2-weighted magnetic resonance imaging (MRI) data. These contrasts capture
information associated with the same underlying anatomy and thus exhibit
similarities. In this paper, we propose a Coupled Dictionary Learning based
multi-contrast MRI reconstruction (CDLMRI) approach to leverage an available
guidance contrast to restore the target contrast. Our approach consists of
three stages: coupled dictionary learning, coupled sparse denoising, and
$k$-space consistency enforcing. The first stage learns a group of dictionaries
that capture correlations among multiple contrasts. By capitalizing on the
learned adaptive dictionaries, the second stage performs joint sparse coding to
denoise the corrupted target image with the aid of a guidance contrast. The
third stage enforces consistency between the denoised image and the
measurements in the $k$-space domain. Numerical experiments on the
retrospective under-sampling of clinical MR images demonstrate that
incorporating additional guidance contrast via our design improves MRI
reconstruction, compared to state-of-the-art approaches.
