Learned spherical ADMM for Rician MRI denoising

A Bilevel Sensitivity-Corrected Reconstruction Framework with Deep Priors for Parallel MRI

A model-driven bilevel optimization framework that couples SENSE-based image reconstruction with SPIRiT-based k-space calibration through shared CSMs, and introduces a deep-prior-guided regularization strategy that preserves the structure of classical linear regularizers while adaptively learning spatially varying regularization weights from denoised intermediate reconstructions.

A Learned ADMM Framework with Fractional-Order Convolutional Regularization for Image Denoising

A Relaxed Gradient Step Denoiser for Splitting Methods in Poisson Inverse Problems

Plug and Play methods combine classical variational models with learned denoisers and have achieved strong results in imaging inverse problems. Their convergence has been widely studied for Gaussian data, whereas Poisson models require additional care because of the nonquadratic Kullback-Leibler fidelity. This work introduces GSDSplit+ , a splitting method built upon PnPSplit+, in which the generic denoising block is replaced by a relaxed Gradient Step Denoiser. The resulting method retains explicit Poisson fidelity updates. The denoiser is defined through the gradient of a learned convex potential parameterized by an Input Convex Neural Network. Its architecture and training promote both blind denoising capability and a smoothness condition sufficient for firm nonexpansiveness. Empirical smoothness estimates are used to select a relaxation parameter compatible with the convergence assumptions of PnPSplit+. Numerical experiments provide evidence that the trained denoiser operates in an FNE-compatible regime on the considered validation data. GSDSplit+ also yields stable reconstructions outside the empirically supported range and shows substantially lower sensitivity to the ADMM parameter, while remaining effective for different blur operators and Poisson noise levels.

Conjugate Gradient Unrolled Network with PSF Conditioning for Non-Diagonal Data Fidelity in CASSI Reconstruction

Deep unfolding methods achieve state-of-the-art performance in coded aperture snapshot spectral imaging (CASSI) reconstruction but typically rely on closed-form data-fidelity updates that assume an ideal optical system. In practical CASSI systems, the field-dependent and wavelength-dependent point spread function (PSF) introduces convolutional coupling that breaks the diagonal structure of the normal equation, rendering closed-form updates inapplicable. We propose a deep unfolding framework that addresses this fundamental algorithmic challenge through three contributions: (1)~a $K$-step conjugate gradient (CG) unrolling that explicitly solves the non-diagonal normal equation under PSF-inclusive forward operators; (2)~a learned gradient refinement module with wavelength-adaptive step sizes generated from a per-wavelength PSF embedding; and (3)~a PSF-conditioned penalty estimator that adapts the ADMM regularization strength to the optical degradation severity. A Monte Carlo PSF training strategy further improves robustness to manufacturing-induced PSF variations. Our method achieves 30.53~dB on the KAIST dataset, +2.73~dB over the DPU baseline (1.27M) using a comparable number of parameters (1.42M), and +1.70~dB over a larger baseline (DPU-B+, 2.12M) using 33\% fewer parameters.

Frozen CLIP Priors for Robust Self-Supervised Poisson Inverse Problems

Self-supervised learning for imaging inverse problems is increasingly important in photon-limited settings, where acquiring clean ground truth is impractical and reconstruction must remain stable under dataset and acquisition shifts. This challenge is amplified under Poisson noise, whose signal-dependent statistics interact with sampling operators (e.g., CFA mosaicing). Meanwhile, foundation vision encoders trained at web scale offer distortion-invariant, content-related representations that generalize well across domains, suggesting a promising route to build priors that transfer beyond the training distribution without expensive fine-tuning. This paper proposes an ADMM-inspired unrolled plug-and-play solver for Poisson inverse problems that decouples a closed-form data-consistency update from a parameter-efficient prior. The prior is implemented as a lightweight decoder operating on frozen CLIP RN50 dense multi-scale features, adapting foundation representations with less trainable parameters. For self-supervision, the method integrates GR2R measurement-domain re-corruption with an Equivariant Imaging regularizer via virtual acquisitions. Experiments on Poisson CFA demosaicing and deblurring show competitive quality, improved robustness under shifts, and self-supervised performance approaching supervised training.

CG-GLORE: A Conjugate Gradient-Based Global-Local Regularization Network for Sparse-View CT Reconstruction

Sparse-view computed tomography (CT) reduces radiation dose by acquiring fewer projection views, but the resulting inverse problem is highly ill-posed and often produces severe streak artifacts. Existing deep reconstruction methods have achieved promising performance, yet many rely on first-order updates or large regularization networks, which can be less effective in ill-conditioned settings. We propose \textbf{CG-GLORE}, a compact deep unrolling framework inspired by second-order optimization for sparse-view CT reconstruction. Each unrolled stage uses a CG-solved linear system based on a structured Hessian surrogate: it retains the physics-induced curvature of the data-fidelity term while using an identity approximation for the learned regularization term. Thus, the method is second-order-inspired rather than an exact Newton method for the full learned objective. To model image priors, we design a Global-Local Regularization Network (GLORE), which combines convolutional local feature extraction with a Long-Range Dependency Representation module based on sparse patchification and Nystr\"{o}m attention. This design captures anatomical details and non-local dependencies while maintaining practical complexity. Experiments on AAPM and DeepLesion under multiple sparse-view and noise settings show that CG-GLORE achieves strong quantitative performance, stable convergence, lower noise power, and improved visual fidelity compared with representative reconstruction methods.