Related papers: MAGPIE: Multilevel-Adaptive-Guided Solver for Ptyc…
Solving non-convex regularized inverse problems is challenging due to their complex optimization landscapes and multiple local minima. However, these models remain widely studied as they often yield high-quality, task-oriented solutions,…
Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
The multi-plane phase retrieval method provides a budget-friendly and effective way to perform phase imaging, yet it often encounters alignment challenges due to shifts along the optical axis in experiments. Traditional methods, such as…
This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
Landscape renderings are realistic images of landscape sites, allowing stakeholders to perceive better and evaluate design ideas. While recent advances in Generative Artificial Intelligence (GAI) enable automated generation of landscape…
Image restoration (IR) is challenging due to the complexity of real-world degradations. While many specialized and all-in-one IR models have been developed, they fail to effectively handle complex, mixed degradations. Recent agentic methods…
Ptychography is an imaging technique that captures multiple overlapping snapshots of a sample, illuminated coherently by a moving localized probe. The image recovery from ptychographic data is generally achieved via an iterative algorithm…
We introduce a novel data reconstruction algorithm known as Gappy auto-encoder (Gappy AE) to address the limitations associated with Gappy proper orthogonal decomposition (Gappy POD), a widely used method for data reconstruction when…
We introduce a probabilistic approach to ptychographic reconstruction in computational imaging. Ptychography is an imaging method where the complex amplitude of an object is estimated from a sequence of diffraction measurements. We…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
Phase retrieval in optical imaging refers to the recovery of a complex signal from phaseless data acquired in the form of its diffraction patterns. These patterns are acquired through a system with a coherent light source that employs a…
Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…
Coherent diffractive imaging (CDI) enables lensless imaging with experimental simplicity and a flexible field of view, yet its resolution is fundamentally constrained by the Abbe diffraction limit. To overcome this limitation, we introduce…
The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…
Learning latent representations that are simultaneously expressive, geometrically well-structured, and reliably calibrated remains a central challenge for Variational Autoencoders (VAEs). Standard VAEs typically assume a diagonal Gaussian…