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We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex…
A simple Gaussian size deconvolution method is routinely used to remove the blur of observed images caused by insufficient angular resolutions of existing telescopes, thereby to estimate the physical sizes of extracted sources and…
Following the earlier verification for Gaussian model in \cite{ASaa2026}, this paper introduces a zero training forward computational framework for the model to realize it in real time applications. The framework is based on discrete…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
We introduce a novel formulation for the evolution of parametric curves by anisotropic curve shortening flow in ${\mathbb R}^d$, $d\geq2$. The reformulation hinges on a suitable manipulation of the parameterization's tangential velocity,…
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variables. One of the functionally separated…
Bayesian full waveform inversion (FWI) offers uncertainty-aware subsurface models; however, posterior sampling directly on observed seismic shot records is rarely practical at the field scale because each sample requires numerous…
Synthetic aperture sonar (SAS) image resolution is constrained by waveform bandwidth and array geometry. Specifically, the waveform bandwidth determines a point spread function (PSF) that blurs the locations of point scatterers in the…
An optical imaging system forms an object image by recollecting light scattered by the object. However, intact optical information of the object delivered through the imaging system is deteriorated by imperfect optical elements and unwanted…
Blind image restoration remains a significant challenge in low-level vision tasks. Recently, denoising diffusion models have shown remarkable performance in image synthesis. Guided diffusion models, leveraging the potent generative priors…
An inverse-free dynamical system is proposed to solve the generalized absolute value equation (GAVE) with a fixed time convergence, where the time of convergence is finite and is uniformly bounded for all initial points. Moreover, an…
Compressed sensing has empowered quality image reconstruction with fewer data samples than previously though possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is a common sparsifying…
Though diffusion models have been successfully applied to various image restoration (IR) tasks, their performance is sensitive to the choice of training datasets. Typically, diffusion models trained in specific datasets fail to recover…
Image deblurring is a classical computer vision problem that aims to recover a sharp image from a blurred image. To solve this problem, existing methods apply the Encode-Decode architecture to design the complex networks to make a good…
Recent advances in image editing with diffusion models have achieved impressive results, offering fine-grained control over the generation process. However, these methods are computationally intensive because of their iterative nature.…
Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to…
In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid)…
Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However,…