Bilevel Learning of Task-Adapted Regularizers

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

UMPIRE-Net: Unrolled Magnitude-Phase Regularization Network for Accelerated MRI

This work proposes UMPIRE-Net (Unrolled Magnitude-Phase In REgularization Network), a PD-DL method that introduces separate learned regularizers for magnitude and phase components, together with a novel data-fidelity formulation that enforces measurements consistency.

Learning phase diversity for solving ill-posed inverse problems in imaging

Inverse problems in imaging are typically ill-posed and are solved using regularized optimization techniques or - in recent times, by employing deep neural networks. While the deep network method enables fast end-to-end reconstruction from raw measurements, it does not necessarily alter the fundamentally ill-posed nature of the underlying inverse problem. It is well known that diverse, non-redundant measurements can improve the robustness of reconstruction algorithms. However, acquiring multiple measurements typically - involves additional hardware and more complex system setups, that may not always be desirable for field deployment. In this work, we note that in both incoherent and coherent (phase retrieval) optical imaging, the irradiance patterns corresponding to two phase diverse measurements associated with the same test object have implicit local correlations, which may be learned by a suitable deep network. A physics informed data augmentation scheme is then described where a trained network is used for generating a phase diverse pseudo-data based on a ground truth data frame, typically acquired using a standard imaging system. We validate this data augmentation approach for both incoherent and coherent optical imaging - configurations, with vortex phase as a - diversity mechanism. Specifically, we observe that the generated pseudo-data closely match the corresponding ground-truth data, with comparable noise characteristics. We further demonstrate that the true data along with the augmented pseudo-data provide- high quality inverse solutions with simpler robust reconstruction algorithms. Our results may open new avenues for leaner, high-fidelity computational imaging systems across a broad range of applications.

Frozen CLIP Priors for Robust Self-Supervised Poisson Inverse Problems

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, implemented as a lightweight decoder operating on frozen CLIP RN50 dense multi-scale features.

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.

Provably Convergent Proximal Gradient Methods with Tailored Input Convex Neural Networks Regularization for Inverse Problems

This study presents a novel Deep Proximal Gradient Descent framework for ill-posed problems by employing a tailored second-order differentiable Input-Convex Neural Networks (ICNNs) as a learned regularizer. A key contribution is the design of convex residual mapping, which preserves the convexity of the regularized objective, thereby enhancing the interpretability of the deep network without sacrificing its expressive power. Based on this framework, we develop two types of algorithms. For linear problems, the ICNN-based regularizer is embedded into the standard proximal gradient structure. For nonlinear problems, we introduce an innovative formulation that employs the learned residual to guide gradient descent, while using the traditional data misfit as a proximal regularizer to avoid network-dominated spurious solutions. Building on this iterative scheme, we establish groundbreaking convergence results for both algorithms, complete with rigorous proofs. Extensive numerical experiments, particularly on real low-dose Computed Tomography data, validate the superior imaging quality and high computational efficiency of our algorithms.