Provably Accelerated Imaging with Restarted Inertia and Score-based Image Priors
This work addresses the need for faster and high-quality image recovery in computational imaging, representing an incremental improvement over prior regularization techniques.
The authors tackled the problem of slow convergence in imaging inverse problems by proposing Restarted Inertia with Score-based Priors (RISP), which accelerates convergence while maintaining high-quality reconstructions, achieving a provably faster stationary-point convergence rate than existing methods like RED.
Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization by denoising (RED), often focus on designing sophisticated image priors to improve reconstruction quality, while leaving convergence acceleration to heuristics. To bridge the gap, we propose Restarted Inertia with Score-based Priors (RISP) as a principled extension of RED. RISP incorporates a restarting inertia for fast convergence, while still allowing score-based image priors for high-quality reconstruction. We prove that RISP attains a faster stationary-point convergence rate than RED, without requiring the convexity of the image prior. We further derive and analyze the associated continuous-time dynamical system, offering insight into the connection between RISP and the heavy-ball ordinary differential equation (ODE). Experiments across a range of imaging inverse problems demonstrate that RISP enables fast convergence while achieving high-quality reconstructions.