A Robust Low-Rank Prior Model for Structured Cartoon-Texture Image Decomposition with Heavy-Tailed Noise

Cartoon-texture image decomposition is a fundamental yet challenging problem in image processing. A significant hurdle in achieving accurate decomposition is the pervasive presence of noise in the observed images, which severely impedes robust results. To address the challenging problem of cartoon-texture decomposition in the presence of heavy-tailed noise, we in this paper propose a robust low-rank prior model. Our approach departs from conventional models by adopting the Huber loss function as the data-fidelity term, rather than the traditional $\ell_2$-norm, while retaining the total variation norm and nuclear norm to characterize the cartoon and texture components, respectively. Given the inherent structure, we employ two implementable operator splitting algorithms, tailored to different degradation operators. Extensive numerical experiments, particularly on image restoration tasks under high-intensity heavy-tailed noise, efficiently demonstrate the superior performance of our model.

Robust Regularized Policy Iteration under Transition Uncertainty

Offline reinforcement learning (RL) enables data-efficient and safe policy learning without online exploration, but its performance often degrades under distribution shift. The learned policy may visit out-of-distribution state-action pairs where value estimates and learned dynamics are unreliable. To address policy-induced extrapolation and transition uncertainty in a unified framework, we formulate offline RL as robust policy optimization, treating the transition kernel as a decision variable within an uncertainty set and optimizing the policy against the worst-case dynamics. We propose Robust Regularized Policy Iteration (RRPI), which replaces the intractable max-min bilevel objective with a tractable KL-regularized surrogate and derives an efficient policy iteration procedure based on a robust regularized Bellman operator. We provide theoretical guarantees by showing that the proposed operator is a $γ$-contraction and that iteratively updating the surrogate yields monotonic improvement of the original robust objective with convergence. Experiments on D4RL benchmarks demonstrate that RRPI achieves strong average performance, outperforming recent baselines including percentile-based methods such as PMDB on the majority of environments while remaining competitive on the rest. Moreover, RRPI exhibits robust behavior. The learned $Q$-values decrease in regions with higher epistemic uncertainty, suggesting that the resulting policy avoids unreliable out-of-distribution actions under transition uncertainty.