plug-and-play reconstruction

Existing imaging inverse problem methods face three key bottlenecks: iterative approaches (e.g., PnP, diffusion-based) suffer from high computational cost and limited performance; unrolled methods exhibit poor generalizability and incur substantial training overhead. This paper proposes a non-iterative, lightweight physics-informed foundation model that unifies diverse tasks—including denoising, deblurring, MRI reconstruction, CT reconstruction, inpainting, and super-resolution. Our core contributions are: (1) the first end-to-end architecture without unrolling, integrating parameterized forward physical models and noise priors; (2) zero-shot cross-task transferability and self-supervised meta-fine-tuning using ≤5 unlabeled images; and (3) feature distillation for efficient model compression. The method achieves state-of-the-art performance on medical, low-light, and microscopy imaging benchmarks, while accelerating inference by over an order of magnitude compared to iterative baselines.

In imaging inverse problems, existing learning-based regularization methods suffer from architectural and training heterogeneity, hindering fair comparative evaluation. To address this, we propose a modular, configurable unified framework that systematically decouples mainstream supervised and unsupervised approaches into interchangeable reconstruction, regularization, and training strategy modules—enabling cross-method, systematic benchmarking. The framework supports end-to-end reproduction and plug-and-play integration, and is validated across CT and MRI reconstruction tasks, demonstrating generality and extensibility. Our key contributions are: (1) the first standardized, open platform for comparative evaluation of learned regularization; (2) empirical characterization of how design choices affect generalization, data efficiency, and physical consistency; and (3) publicly available code and detailed reproducibility guidelines, establishing a community benchmark and principled design paradigm for future research.

This study addresses the inherent trade-off in inverse problems between guaranteed convergence and high-quality reconstruction by proposing a novel method that integrates a generative denoiser with a tailored noise decay schedule. This work is the first to incorporate the multi-stage denoising capabilities of diffusion or flow models into a first-order optimization framework, rigorously ensuring algorithmic convergence to the Bayesian maximum a posteriori (MAP) estimate while substantially enhancing reconstruction quality. By doing so, it bridges the gap between theoretical convergence guarantees and the empirical performance of generative priors. Experimental results demonstrate that the proposed approach outperforms conventional methods with provable convergence across various ill-posed inverse problems, achieving performance on par with state-of-the-art empirical techniques.

To address the ill-posed inverse problem in single-pixel imaging, this paper proposes a Plug-and-Play Denoising Diffusion Implicit Model (PnP-DDIM) framework. Methodologically, we decouple the DDIM diffusion process into an interpretable three-stage paradigm—denoising, data-consistency correction, and sampling—and introduce a hybrid data-consistency module that linearly fuses multiple PnP fidelity terms to directly refine the denoiser output, thereby enhancing measurement consistency while preserving diffusion trajectory stability. Our key contribution is the first deep integration of the plug-and-play mechanism into the DDIM sampling procedure, enabling end-to-end co-optimization of learned priors and physical forward models. Experiments demonstrate significant improvements in reconstruction quality across multiple sampling rates (average PSNR gain of +1.8 dB), along with enhanced convergence robustness, outperforming state-of-the-art methods including PnP-ADMM and DiffPIR.

This work addresses the lack of a unified theoretical foundation for learned iterative networks in computational imaging and inverse problems. We propose a continuous-domain reconstruction framework grounded in operator learning, which explicitly decouples *how to compute* (algorithmic architecture) from *what to compute* (the reconstruction operator), thereby bridging the theoretical gap between classical optimization-based methods and data-driven models. Methodologically, we integrate variational unfolding, operator modeling in function spaces, deep neural network parameterization, and end-to-end training into a single coherent framework—yielding a learnable, interpretable, and generalizable reconstruction operator. Our approach unifies major classes of learned iterative methods under a common theoretical umbrella. Extensive numerical experiments validate its effectiveness. The framework establishes a new paradigm for designing reconstruction networks that simultaneously offer rigorous theoretical guarantees and strong practical performance.

This study addresses the disconnect between theory and practice in plug-and-play (PnP) image restoration, where existing convergence analyses typically assume fixed noise levels, contradicting practical annealing strategies. To bridge this gap, we establish rigorous convergence guarantees for PnP algorithms employing decreasing noise levels. Our core contribution is the first proof of asymptotic stationarity with respect to a terminal denoising objective for a broad class of PnP frameworks—including RED, PGD, and SNORE—without requiring predefined decay rates, thereby unifying theoretical analysis across deterministic and stochastic optimization settings. Experiments demonstrate that this annealing strategy achieves the theoretically predicted convergence behavior and significantly improves restoration performance across various inverse problems, including image inpainting and super-resolution.

This work addresses the instability of pretrained deep denoisers in Plug-and-Play (PnP) and Regularization by Denoising (RED) iterative reconstruction, where local instabilities often lead to “spike-and-collapse” behavior and reconstruction failure. The study formally characterizes this instability for the first time and introduces a lightweight stabilization framework that requires no modification or retraining of the original denoiser. By incorporating a learnable contraction anchor operator grounded in contraction mapping theory and adaptive regularization, the method dynamically suppresses unstable regions during PnP/RED iterations. Compatible with various proximal algorithms and denoiser architectures, the approach consistently achieves collapse-free, high-quality reconstructions across diverse imaging tasks, noise levels, and network designs, substantially enhancing the reliability and practicality of PnP and RED methodologies.

This work investigates the fundamental performance limits of learned variational regularizers for linear inverse problems under unknown noise statistics. Addressing the bottleneck that existing methods fail to approach the optimal affine estimator, we systematically analyze the theoretical performance gaps among Tikhonov, Lavrentiev, and general quadratic regularization under non-white noise. Our analysis reveals that the noise model critically determines the efficacy of regularization structure: even within the same functional framework, distinct regularizer forms induce significant performance disparities. Through rigorous theoretical derivation and numerical experiments, we quantify— for the first time—the performance degradation incurred when noise statistics are not jointly learned with the regularizer, proving this loss to be non-negligible. The key contribution is the formal identification of an inherent performance gap arising from learning the regularizer alone, without explicit noise modeling; only joint learning of both the regularization structure and the noise model enables convergence to the optimal affine solution.

Traditional Plug-and-Play Priors (PnP) methods embed denoising priors solely in the image domain, limiting their ability to preserve structural details. To address this, this work pioneers the extension of the PnP framework to the *analysis domain*—specifically, the gradient domain—introducing Analysis-domain PnP (APnP). Our key innovation is a learnable gradient-domain denoiser, formulated as a data-driven, analysis-based total variation regularization. Leveraging this implicit prior, we develop two efficient reconstruction algorithms: APnP-HQS and APnP-ADMM. Extensive experiments on image deblurring and super-resolution demonstrate that APnP achieves performance on par with conventional image-domain PnP methods, while offering superior edge preservation and stronger theoretical consistency. These results validate the effectiveness, feasibility, and practical utility of the analysis-domain PnP paradigm.

This study addresses the limitation of plug-and-play methods, where directly substituting proximal operators compromises variational interpretability and precludes convergence guarantees. To overcome this, we propose the Learned Proximal Network (LPN), which leverages architectural design to ensure that the denoiser strictly corresponds to the proximal operator of a regularizer. Furthermore, we extend the theoretical framework to a broader class of activation functions, analytically characterize the mean-induced regularization mechanism, and develop an operator scaling technique with provable convergence guarantees. Consequently, this work restores both the variational interpretation and convergence properties of the algorithm while maintaining state-of-the-art reconstruction quality, thereby providing rigorous theoretical foundations for plug-and-play approaches.