Alternating minimization approach for multi-frame image reconstruction
There are a variety of imaging modalities that record a sequence of measurements where the sensor and/or the objects in the scene are moving and the goal is to reconstruct an image without motion blur. Examples include multi-frame super-resolution problems and motion-compensated image reconstruction problems in medical imaging. Various methods have been proposed for such applications, often in the context of specific imaging modalities. However, many such methods can be formulated in a common framework and thus solved by the same optimization method. To solve the reconstruction problem efficiently, the optimization method must be designed carefully. This paper proposes a novel approach to solve multi-frame image reconstruction problems more efficiently. We use a variable-splitting technique to dissociate the original problem into a few simpler problems that are then solved individually using an alternating minimization method. The proposed method is amenable to preconditioning, parallelization, and application of block iterative algorithms to the sub-problems. Simulation results demonstrate that even with simple diagonal or circulant preconditioners, the proposed method converges faster than the conjugate gradient (CG) method.