Accelerated MR parameter mapping with a union of local subspaces constraint

Purpose A new reconstruction method for multi‐contrast imaging and parameter mapping based on a union of local subspaces constraint is presented. Theory Subspace constrained reconstructions use a predetermined subspace to explicitly constrain the relaxation signals. The choice of subspace size (K) impacts the approximation error vs noise‐amplification tradeoff associated with these methods. A different approach is used in the model consistency constraint (MOCCO) framework to leverage the subspace model to enforce a softer penalty. Our proposed method, MOCCO‐LS, augments the MOCCO model with a union of local subspaces (LS) approach. The union of local subspaces model is coupled with spatial support constraints and incorporated into the MOCCO framework to regularize the contrast signals in the scene. Methods The performance of the MOCCO‐LS method was evaluated in vivo on T1 and T2 mapping of the human brain and with Monte‐Carlo simulations and compared against MOCCO and the explicit subspace constrained models. Results The results demonstrate a clear improvement in the multi‐contrast images and parameter maps. We sweep across the model order space (K) to compare the different reconstructions and demonstrate that the reconstructions have different preferential operating points. Experiments on T2 mapping show that the proposed method yields substantial improvements in performance even when operating at very high acceleration rates. Conclusions The use of a union of local subspace constraints coupled with a sparsity promoting penalty leads to improved reconstruction quality of multi‐contrast images and parameter maps.