In magnetic resonance imaging, multiple contrasts are exploited to extract clinically relevant tissue parameters and pathological tissue changes. Multi-contrast acquisitions find important applications in parameter mapping (e.g. T1 and T2 mapping) and magnetic resonance fingerprinting. However, these acquisitions lead to long scan times since multiple images with different contrasts need to be acquired. In this study, we present a new reconstruction technique, termed as High-Dimensionality undersampled Patch-based RecOnSTruction (HD-PROST), for highly accelerated 2D and 3D multi-channel multi-contrast MRI.