Deliang Wei

Deliang Wei, Peng Chen, Fang Li

Deep denoisers have shown excellent performance in solving inverse problems in signal and image processing. In order to guarantee the convergence, the denoiser needs to satisfy some Lipschitz conditions like non-expansiveness. However, enforcing such constraints inevitably compromises recovery performance. This paper introduces a novel training strategy that enforces a weaker constraint on the deep denoiser called pseudo-contractiveness. By studying the spectrum of the Jacobian matrix, relationships between different denoiser assumptions are revealed. Effective algorithms based on gradient descent and Ishikawa process are derived, and further assumptions of strict pseudo-contractiveness yield efficient algorithms using half-quadratic splitting and forward-backward splitting. The proposed algorithms theoretically converge strongly to a fixed point. A training strategy based on holomorphic transformation and functional calculi is proposed to enforce the pseudo-contractive denoiser assumption. Extensive experiments demonstrate superior performance of the pseudo-contractive denoiser compared to related denoisers. The proposed methods are competitive in terms of visual effects and quantitative values.

Deliang Wei, Peng Chen, Haobo Xu et al.

Plug-and-play (PnP) methods with deep denoisers have shown impressive results in imaging problems. They typically require strong convexity or smoothness of the fidelity term and a (residual) non-expansive denoiser for convergence. These assumptions, however, are violated in Poisson inverse problems, and non-expansiveness can hinder denoising performance. To address these challenges, we propose a cocoercive conservative (CoCo) denoiser, which may be (residual) expansive, leading to improved denoising. By leveraging the generalized Helmholtz decomposition, we introduce a novel training strategy that combines Hamiltonian regularization to promote conservativeness and spectral regularization to ensure cocoerciveness. We prove that CoCo denoiser is a proximal operator of a weakly convex function, enabling a restoration model with an implicit weakly convex prior. The global convergence of PnP methods to a stationary point of this restoration model is established. Extensive experimental results demonstrate that our approach outperforms closely related methods in both visual quality and quantitative metrics.

Peng Chen, Deliang Wei, Jiale Yao et al.

Missing entries in multi dimensional data pose significant challenges for downstream analysis across diverse real world applications. These data are naturally represented as tensors, and recent completion methods integrating global low rank priors with plug and play denoisers have demonstrated strong empirical performance. However, these approaches often rely on empirical convergence alone or unrealistic assumptions, such as deep denoisers acting as proximal operators of implicit regularizers, which generally does not hold. To address these limitations, we propose a novel tensor completion framework grounded in the monotone inclusion paradigm. Within this framework, deep denoisers are treated as general operators that require far fewer restrictions than in classical optimization based formulations. To better capture holistic structure, we further incorporate generalized low rank priors with weakly convex penalties. Building upon the Davis Yin splitting scheme, we develop the GTCTV DPC algorithm and rigorously establish its global convergence. Extensive experiments demonstrate that GTCTV DPC consistently outperforms existing methods in both quantitative metrics and visual quality, particularly at low sampling rates. For instance, at a sampling rate of 0.05 for multi dimensional image completion, GTCTV DPC achieves an average mean peak signal to noise ratio (MPSNR) that surpasses the second best method by 0.717 dB, and 0.649 dB for multi spectral images, and color videos, respectively.

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.