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Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…
Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model,…
Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The…
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…
Magnetic Resonance Imaging (MRI) is a critical tool in modern medical diagnostics, yet its prolonged acquisition time remains a critical limitation, especially in time-sensitive clinical scenarios. While undersampling strategies can…
Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…
Recent advancements in artificial intelligence have created transformative capabilities in image synthesis and generation, enabling diverse research fields to innovate at revolutionary speed and spectrum. In this study, we leverage this…
MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions. This ambiguity becomes more severe under high acceleration, where pixel-domain continuous predictors tend to…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…
Denoising diffusion models have gained popularity as a generative modeling technique for producing high-quality and diverse images. Applying these models to downstream tasks requires conditioning, which can take the form of text, class…
Objective: This paper investigates how generative models, trained on ground-truth images, can be used \changes{as} priors for inverse problems, penalizing reconstructions far from images the generator can produce. The aim is that learned…
A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…
Inspired by their success in solving challenging inverse problems in computer vision, implicit neural representations (INRs) have been recently proposed for reconstruction in low-dose/sparse-view X-ray computed tomography (CT). An INR…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…
Neural fields are a highly effective representation across visual computing. This work observes that fitting these fields is greatly improved by incorporating spatial stochasticity during training, and that this simple technique can replace…
Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements…
Small animal PET scanners require high spatial resolution and good sensitivity. To reconstruct high-resolution images in 3D-PET, iterative methods, such as OSEM, are superior to analytical reconstruction algorithms, although their high…
Accurate multi-slice reconstruction from limited measurement data is crucial to speed up the acquisition process in medical and scientific imaging. However, it remains challenging due to the ill-posed nature of the problem and the high…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…