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Regression analysis-based approaches have been widely studied for face recognition (FR) in the past several years. More recently, to better deal with some difficult conditions such as occlusions and illumination, nuclear norm based matrix…

Numerical Analysis · Mathematics 2020-01-30 Jifei Miao , Kit Ian Kou

Low-dose Computed Tomography is a common issue in reality. Current reduction, sparse sampling and limited-view scanning can all cause it. Between them, limited-view CT is general in the industry due to inevitable mechanical and physical…

Image and Video Processing · Electrical Eng. & Systems 2021-01-20 Ken Deng , Chang Sun , Yitong Liu , Hongwen Yang

The task of image restration is to find the spatial correspondence of two or more given images. In this paper we assume that the correspondence is given either by an Euclidean, or by an affine volume-preserving transformation. Since the…

Optimization and Control · Mathematics 2010-07-30 Martin Schröter , Uwe Helmke , Otto Sauer

Dynamic imaging is essential for analyzing various biological systems and behaviors but faces two main challenges: data incompleteness and computational burden. For many imaging systems, high frame rates and short acquisition times require…

Image and Video Processing · Electrical Eng. & Systems 2024-06-12 Luke Lozenski , Mark A. Anastasio , Umberto Villa

A common task in single particle electron cryomicroscopy (cryo-EM) is the rigid alignment of images and/or volumes. In the context of images, a rigid alignment involves estimating the inner-product between one image of $N\times N$ pixels…

Numerical Analysis · Mathematics 2022-12-07 Aaditya V. Rangan

We derive and showcase a novel approach to approximating Fourier transforms in higher dimensions, focusing specifically on the case of 2D radially concentrated ('ring-like') functions. We first reduce the problem to that of evaluating the…

High Energy Astrophysical Phenomena · Physics 2026-04-08 Filip Niewiński , Michael D. Johnson

Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear…

Numerical Analysis · Mathematics 2016-04-07 Simon Maretzke , Matthias Bartels , Martin Krenkel , Tim Salditt , Thorsten Hohage

We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem…

Numerical Analysis · Mathematics 2017-12-11 Yunmei Chen , Ruogu Fang , Xiaojing Ye

Recently regression analysis becomes a popular tool for face recognition. The existing regression methods all use the one-dimensional pixel-based error model, which characterizes the representation error pixel by pixel individually and thus…

Computer Vision and Pattern Recognition · Computer Science 2014-05-07 Jian Yang , Jianjun Qian , Lei Luo , Fanlong Zhang , Yicheng Gao

The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…

Functional Analysis · Mathematics 2025-02-06 Duo Liu , Gangrong Qu , Shan Gao

In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…

Numerical Analysis · Mathematics 2018-03-28 Martin Burger , Hendrik Dirks , Lena Frerking , Andreas Hauptmann , Tapio Helin , Samuli Siltanen

A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…

Numerical Analysis · Mathematics 2022-05-13 Yao Xiao , Jan Glaubitz , Anne Gelb , Guohui Song

Tomography is a central tool in medical applications, allowing doctors to investigate patients' interior features. The Radon transform (in two dimensions) is commonly used to model the measurement process in parallel-beam CT. Suitable…

Numerical Analysis · Mathematics 2026-02-27 Richard Huber

Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…

Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…

Numerical Analysis · Mathematics 2025-10-17 Richard Huber

For Machine Learning (ML) classification problem, where a vector of $\mathbf{x}$--observations (values of attributes) is mapped to a single $y$ value (class label), a generalized Radon--Nikodym type of solution is proposed.…

Machine Learning · Computer Science 2015-12-16 Vladislav Gennadievich Malyshkin

Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits.…

Optics · Physics 2015-05-13 S. Marchesini

One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…

Numerical Analysis · Mathematics 2020-04-02 Alexander Barnett , Charles L. Epstein , Leslie Greengard , Jeremy Magland

We propose a variational approach to obtain super-resolution images from multiple low-resolution frames extracted from video clips. First the displacement between the low-resolution frames and the reference frame are computed by an optical…

Computer Vision and Pattern Recognition · Computer Science 2017-04-21 Rui Zhao , Raymond H. Chan

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

Analysis of PDEs · Mathematics 2018-08-01 Ngoc Do , Leonid Kunyansky