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Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Machine Learning · Computer Science 2025-08-05 Hyungjin Chung , Jeongsol Kim , Jong Chul Ye

Recovering images from optical interferometric observations is one of the major challenges in the field. Unlike the case of observations at radio wavelengths, in the optical the atmospheric turbulence changes the phases on a very short time…

We address the problem of restoring a high-quality image from an observed image sequence strongly distorted by atmospheric turbulence. A novel algorithm is proposed in this paper to reduce geometric distortion as well as…

Computer Vision and Pattern Recognition · Computer Science 2017-09-20 Chun Pong Lau , Yu Hin Lai , Lok Ming Lui

Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…

Computer Vision and Pattern Recognition · Computer Science 2016-05-20 Teodora Szasz , Adrian Basarab , Denis Kouamé

The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…

Information Retrieval · Computer Science 2022-05-25 Zhenan Fan , Halyun Jeong , Babhru Joshi , Michael P. Friedlander

The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…

Machine Learning · Computer Science 2024-07-29 Jaesung Choi , Pilwon Kim

Multi-sentence summarization is a well studied problem in NLP, while generating image descriptions for a single image is a well studied problem in Computer Vision. However, for applications such as image cluster labeling or web page…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Nicholas Trieu , Sebastian Goodman , Pradyumna Narayana , Kazoo Sone , Radu Soricut

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

Optimization and Control · Mathematics 2021-11-10 Andreas Habring , Martin Holler

In this paper, we propose to improve image decomposition algorithms in the case of noisy images. In \cite{gilles1,aujoluvw}, the authors propose to separate structures, textures and noise from an image. Unfortunately, the use of separable…

Image and Video Processing · Electrical Eng. & Systems 2024-11-12 Jerome Gilles

We address the estimation of seismic wavefields by means of Multidimensional Deconvolution (MDD) for various redatuming applications. While offering more accuracy than conventional correlation-based redatuming methods, MDD faces challenges…

Numerical Analysis · Mathematics 2024-04-03 Daria Sushnikova , Matteo Ravasi , David Keyes

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

Image and Video Processing · Electrical Eng. & Systems 2020-08-26 Andreas Kofler , Markus Haltmeier , Tobias Schaeffter , Marc Kachelrieß , Marc Dewey , Christian Wald , Christoph Kolbitsch

We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…

Analysis of PDEs · Mathematics 2022-09-20 Florian Faucher , Otmar Scherzer

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their…

Computational Engineering, Finance, and Science · Computer Science 2017-09-01 Emmanuel Soubies , Thanh-An Pham , Michael Unser

We present Decomposer, a semi-supervised reconstruction model that decomposes distorted image sequences into their fundamental building blocks - the original image and the applied augmentations, i.e., shadow, light, and occlusions. To solve…

Computer Vision and Pattern Recognition · Computer Science 2023-11-29 Boris Meinardus , Mariusz Trzeciakiewicz , Tim Herzig , Monika Kwiatkowski , Simon Matern , Olaf Hellwich

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An…

Geophysics · Physics 2009-11-13 Ignace Loris , Guust Nolet , Ingrid Daubechies , F. A. Dahlen

Approximate deconvolution forms a mathematical framework for the structural modeling of turbulence. The sub-filter scale flow quantities are typically recovered by using the Van Cittert iterative procedure. In this paper, however, we put…

Fluid Dynamics · Physics 2017-07-31 Omer San , Prakash Vedula

Due to the lack of a definitive ground truth for the image fusion problem, the loss functions are structured based on evaluation metrics, such as the structural similarity index measure (SSIM). However, in doing so, a bias is introduced…

Computer Vision and Pattern Recognition · Computer Science 2024-04-25 Aytekin Erdogan , Erdem Akagündüz

Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…

Optimization and Control · Mathematics 2023-11-29 Nina Maria Gottschling , Paolo Campodonico , Vegard Antun , Anders C. Hansen

The free-form deformation model can represent a wide range of non-rigid deformations by manipulating a control point lattice over the image. However, due to a large number of parameters, it is challenging to fit the free-form deformation…

Computer Vision and Pattern Recognition · Computer Science 2022-06-10 Takumi Nakane , Haoran Xie , Chao Zhang

This article addresses the image denoising problem in the situations of strong noise. We propose a dual sparse decomposition method. This method makes a sub-dictionary decomposition on the over-complete dictionary in the sparse…

Computer Vision and Pattern Recognition · Computer Science 2017-04-25 Hong Sun , Chen-guang Liu , Cheng-wei Sang