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A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\rightarrow\mathbb{C}$ from its continuous short time Fourier transform…

Numerical Analysis · Mathematics 2017-06-07 Sami Merhi , Aditya Viswanathan , Mark Iwen

In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and…

Numerical Analysis · Mathematics 2025-10-20 Joseph Morlier

We analyze integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component…

Analysis of PDEs · Mathematics 2020-02-04 Manuel Friedrich , Francesco Solombrino

A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.…

Computer Vision and Pattern Recognition · Computer Science 2014-03-14 Huazhong Shu , Jian Zhou , Guo-Niu Han , Limin M. Luo , Jean-Louis Coatrieux

The reconstruction of an unknown function $f$ from its line sums is the aim of discrete tomography. However, two main aspects prevent reconstruction from being an easy task. In general, many solutions are allowed due to the presence of the…

Combinatorics · Mathematics 2021-04-20 Matthew Ceko , Silvia M. C. Pagani , Rob Tijdeman

Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…

Information Theory · Computer Science 2017-02-22 Cheng Cheng , Junzheng Jiang , Qiyu Sun

This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…

Analysis of PDEs · Mathematics 2012-03-07 Guillaume Bal , Gunther Uhlmann

Sampling recovery on some function classes is studied in this paper. Typically, function classes are defined by imposing smoothness conditions. It was understood in nonlinear approximation that structural conditions in the form of control…

Numerical Analysis · Mathematics 2024-06-27 V. Temlyakov

In this paper, we deal with the problem of reconstruction from Radon random samples in local shift-invariant signal space. Different from sampling after Radon transform, we consider sampling before Radon transform, where the sample set is…

Optimization and Control · Mathematics 2025-11-05 Zhanpeng Deng , Jiao Li , Jun Xian

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an…

Computer Vision and Pattern Recognition · Computer Science 2016-08-10 Roberto Tron

This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches…

Signal Processing · Electrical Eng. & Systems 2026-01-14 Neil Irwin Bernardo

We show that the classical Prony's method for recovery of a sparse signal from its consecutive Fourier coefficients can be viewed as a spectral identification problem for an unknown restriction of a known linear operator. This presents a…

Functional Analysis · Mathematics 2024-03-29 Ilya A. Krishtal , Götz E. Pfander

Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…

Complex Variables · Mathematics 2015-11-17 Lander Cnudde , Hendrik De Bie

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a…

Optimization and Control · Mathematics 2017-04-11 Irène Waldspurger

Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in…

Computer Vision and Pattern Recognition · Computer Science 2022-02-22 Dong Xiao , Siyou Lin , Zuoqiang Shi , Bin Wang

To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…

Numerical Analysis · Mathematics 2015-01-14 Julian Schmid , Thomas Glatz , Behrooz Zabihian , Mengyang Liu , Wolfgang Drexler , Otmar Scherzer

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…

Information Theory · Computer Science 2013-11-08 Emmanuel Candes , Xiaodong Li , Mahdi Soltanolkotabi

In this study, we propose a generalized turbo signal recovery algorithm to estimate a signal from quantized measurements, in which the sensing matrix is a row-orthogonal matrix, such as the partial discrete Fourier transform matrix. The…

Information Theory · Computer Science 2016-11-17 Ting Liu , Chao-Kai Wen , Shi Jin , Xiaohu You

We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…

Optimization and Control · Mathematics 2024-07-19 Vasileios Charisopoulos , Rebecca Willett

A semilinear parabolic problem of second order with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is…

Analysis of PDEs · Mathematics 2014-06-19 R. H. De Staelen , M. Slodička