Yu Sun

Marien Renaud, Julien Hermant, Deliang Wei et al.

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.

Yuan Gao, Wenhan Guo, Yu Sun

Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the object -- necessitating effective image prior to regularize the inference. In this paper, we propose a regularized neural field (NF) approach which integrates the denoising score function used in score-based generative models. The neural field formulation offers convenient flexibility to performing joint estimation, while the denoising score function imposes the rich structural prior of images. Our results on three high-contrast simulated objects show that the proposed approach yields a better imaging quality compared to the state-of-the-art NF approach, where regularization is based on total variation.