One-Step Image Reconstruction for Cine MRI with a Quadratic Constraint

Motivation: In cine MRI, the measurements within each time-frame alone are too noisy for image reconstruction. Some information must be ‘borrowed’ from other time frames and the reconstruction algorithm is a slow iterative procedure. Goal(s): We set up a constrained objective function, which uses the measurements at other time frames to regularize the image reconstruction. We derive a non-iterative algorithm to minimize this objective function. Approach: The derivation of the algorithm is based on the calculus of variations. The resultant algorithm is in the form of filtered backprojection. Results: The feasibility of the proposed algorithm is demonstrated with a clinical patient brain study. Impact: Non-iterative reconstruction that minimizes a constrained objective function increases the throughput in healthcare institutions. This translates to reduced healthcare costs. The new reconstruction formula has a closed-form explicit expression of how to incorporate the reference image in dynamic reconstruction.