Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging problems, specifically, their dual problems, for which we develop in detail the relevant coarse-grid problems. We demonstrate the performance of our method on total variation denoising and magnetic resonance imaging.

翻译：基于非光滑一致性条件，我们构建并证明了一种在前向-后向分裂方法中交替使用细网格与粗网格步骤的收敛性。本研究聚焦于总变差正则化的逆成像问题，特别是其对应的对偶问题，并针对该问题详细推导了相关的粗网格问题。我们通过总变差去噪和磁共振成像两个应用场景验证了所提方法的性能。