Why do we regularise in every iteration for imaging inverse problems?
This work addresses computational efficiency for researchers and practitioners in imaging inverse problems, but it is incremental as it adapts an existing method to a new domain.
The paper tackles the computational overhead of regularisation in iterative methods for imaging inverse problems by applying the ProxSkip algorithm, which randomly skips regularisation steps, and proposes a novel PDHGSkip version, achieving accelerated computations while maintaining high-quality reconstructions.
Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational overhead since such evaluation can be costly. In this context, the ProxSkip algorithm, recently proposed for federated learning purposes, emerges as an solution. It randomly skips regularisation steps, reducing the computational time of an iterative algorithm without affecting its convergence. Here we explore for the first time the efficacy of ProxSkip to a variety of imaging inverse problems and we also propose a novel PDHGSkip version. Extensive numerical results highlight the potential of these methods to accelerate computations while maintaining high-quality reconstructions.