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The combination of tomographic imaging and deep learning, or machine learning in general, promises to empower not only image analysis but also image reconstruction. The latter aspect is considered in this perspective article with an…

Quantitative Methods · Quantitative Biology 2016-11-07 Ge Wang

The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…

Image and Video Processing · Electrical Eng. & Systems 2021-06-29 Sanjay Viswanath , Manu Ghulyani , Muthuvel Arigovindan

In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…

Optimization and Control · Mathematics 2022-06-10 Jongho Park

Interferometric Synthetic Aperture Radar (InSAR) Imaging methods are usually based on algorithms of match-filtering type, without considering the scene's characteristic, which causes limited imaging quality. Besides, post-processing steps…

Signal Processing · Electrical Eng. & Systems 2022-10-07 Xu Zhan , Xiaoling Zhang , Shunjun Wei , Jun Shi

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…

Image and Video Processing · Electrical Eng. & Systems 2023-08-28 Alexis Goujon , Sebastian Neumayer , Pakshal Bohra , Stanislas Ducotterd , Michael Unser

We propose a new type of regularization functional for images called oscillation total generalized variation (TGV) which can represent structured textures with oscillatory character in a specified direction and scale. The infimal…

Numerical Analysis · Mathematics 2018-09-17 Yiming Gao , Kristian Bredies

Remote sensing image retrieval (RSIR) is the process of ranking database images depending on the degree of similarity compared to the query image. As the complexity of RSIR increases due to the diversity in shooting range, angle, and…

Computer Vision and Pattern Recognition · Computer Science 2020-10-20 Hyunseung Chung , Woo-Jeoung Nam , Seong-Whan Lee

Received signal strength based radio tomographic imaging is a popular device-free indoor localization method which reconstructs the spatial loss field of the environment using measurements from a dense wireless network. Existing methods…

Emerging Technologies · Computer Science 2016-04-12 Hüseyin Yiğitler , Riku Jäntti , Ossi Kaltiokallio , Neal Patwari

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…

Numerical Analysis · Mathematics 2022-07-12 Junfeng Yin , Nan Li , Ning Zheng

Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction…

Optimization and Control · Mathematics 2019-06-14 Hung Nien , Jeffrey A. Fessler

Tomography has made a revolutionary impact on diverse fields, ranging from macro-/mesoscopic scale studies in biology, radiology, plasma physics to the characterization of 3D atomic structure in material science. The fundamental of…

Optimization and Control · Mathematics 2020-04-28 Minh Pham , Yakun Yuan , Arjun Rana , Jianwei Miao , Stanley Osher

Magnetic resonance imaging (MRI) reconstruction is a fundamental task aimed at recovering high-quality images from undersampled or low-quality MRI data. This process enhances diagnostic accuracy and optimizes clinical applications. In…

Image and Video Processing · Electrical Eng. & Systems 2025-03-11 Xiaoyan Kui , Zijie Fan , Zexin Ji , Qinsong Li , Chengtao Liu , Weixin Si , Beiji Zou

Magnetic resonance imaging (MRI) is a versatile imaging technique that allows different contrasts depending on the acquisition parameters. Many clinical imaging studies acquire MRI data for more than one of these contrasts---such as for…

Numerical Analysis · Mathematics 2017-10-06 Matthias J. Ehrhardt , Marta M. Betcke

We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…

Neural and Evolutionary Computing · Computer Science 2020-11-03 Talgat Daulbaev , Alexandr Katrutsa , Larisa Markeeva , Julia Gusak , Andrzej Cichocki , Ivan Oseledets

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

Complex Variables · Mathematics 2010-11-17 Nicholas Hoell , Guillaume Bal

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion).…

In this article, we revisit iterative methods for solving the inverse problem of photoacoustic tomography in free space. Recently, there have been interesting developments on explicit formulations of the adjoint operator, demonstrating that…

Analysis of PDEs · Mathematics 2017-05-16 Markus Haltmeier , Linh V. Nguyen

Total-variation (TV)-based Computed Tomography (CT) image reconstruction has shown experimentally to be capable of producing accurate reconstructions from sparse-view data. In particular TV-based reconstruction is very well suited for…

Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…

Optimization and Control · Mathematics 2011-10-25 Nelly Pustelnik , Caroline Chaux , Jean-Christophe Pesquet

Image co-segmentation is important for its advantage of alleviating the ill-pose nature of image segmentation through exploring the correlation between related images. Many automatic image co-segmentation algorithms have been developed in…

Computer Vision and Pattern Recognition · Computer Science 2019-11-19 Xiabi Liu , Xin Duan
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