Iterative Operator Sketching Framework for Large-Scale Imaging Inverse Problems

Despite impressive empirical performance in various imaging applications, iterative data-driven reconstruction (IDR) schemes such as plug-and-play algorithms and deep unrolling networks can have significant computational limitations, especially for large-scale imaging inverse problems. This is mostly because they need to involve the high-dimensional forward/adjoint operators that are expensive to compute in each iteration. In this work, we propose a new operator sketching framework tailored for designing efficient IDR schemes, which are currently state-of-the-art solutions for imaging inverse problems. Our framework performs dimensionality reduction in both image and measurement data domains, leading to efficient computations. Using this framework, we derive several accelerated IDR schemes, such as the plug-and-play multi-stage sketched gradient (PnP-MS2G) and sketching-based primal-dual (LSPD and Sk-LSPD) deep unrolling networks. Our experiments on X-ray CT image reconstruction demonstrate the remarkable effectiveness of the proposed sketched IDR methods.