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Related papers: Sparse regularization in limited angle tomography

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Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along…

Image and Video Processing · Electrical Eng. & Systems 2022-04-22 Siiri Rautio , Rashmi Murthy , Tatiana A. Bubba , Matti Lassas , Samuli Siltanen

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…

Optimization and Control · Mathematics 2008-03-25 François-Xavier Dupé , Jalal Fadili , Jean Luc Starck

Image quality is the basis of image communication and understanding tasks. Due to the blur and noise effects caused by imaging, transmission and other processes, the image quality is degraded. Blind image restoration is widely used to…

Image and Video Processing · Electrical Eng. & Systems 2021-01-26 Ningshan Xu

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Mathematical Physics · Physics 2023-05-03 M. H. Ding , H. Y. Liu , G. H. Zheng

In this paper we consider the reconstruction problem of photoacoustic tomography (PAT) with a flat observation surface. We develop a direct reconstruction method that employs regularization with wavelet sparsity constraints. To that end, we…

Optimization and Control · Mathematics 2017-03-27 Jürgen Frikel , Markus Haltmeier

Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate…

Instrumentation and Methods for Astrophysics · Physics 2019-02-27 R. Joseph , F. Courbin , J. -L. Starck , S. Birrer

Classical total variation (TV) based iterative reconstruction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a…

Medical Physics · Physics 2018-03-06 Peng Bao , Jiliu Zhou , Yi Zhang

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Optimization and Control · Mathematics 2014-12-09 Samuel Vaiter , Gabriel Peyré , Jalal M. Fadili

Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…

Image and Video Processing · Electrical Eng. & Systems 2023-11-30 Cesar F. Caiafa , Ramiro M. Irastorza

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

Information Theory · Computer Science 2021-02-17 Pengxia Wu , Hui Ma , Julian Cheng

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…

Numerical Analysis · Mathematics 2020-01-13 Simon Hubmer , Kim Knudsen , Changyou Li , Ekaterina Sherina

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

Statistics Theory · Mathematics 2012-04-03 Klaus Frick , Philipp Marnitz , Axel Munk

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Numerical Analysis · Mathematics 2025-05-12 Abinash Nayak

Sparse-view computed tomography (CT) is an effective method to reduce the radiation exposure in medical imaging. To reduce the severe streaking artifacts that occur in reconstructed images due to violation of the Nyquist/Shannon sampling…

Medical Physics · Physics 2026-03-17 Huiying Li , Yizhuang Song

Faraday tomography (or rotation measure synthesis) is a procedure to convert linear polarization spectra into the Faraday dispersion function, which provides us with unique information of magneto-ionic media along the line of sight.…

Instrumentation and Methods for Astrophysics · Physics 2018-12-03 Kazunori Akiyama , Takuya Akahori , Yoshimitsu Miyashita , Shinsuke Ideguchi , Ryosuke Yamaguchi , Shiro Ikeda , Keitaro Takahashi

Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

Numerical Analysis · Mathematics 2024-06-26 Andrea Ebner , Matthias Schwab , Markus Haltmeier

We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…

Numerical Analysis · Mathematics 2019-12-13 Jürgen Frikel , Markus Haltmeier

We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…

Optimization and Control · Mathematics 2019-04-02 Lukas F. Lang , Sebastian Neumayer , Ozan Öktem , Carola-Bibiane Schönlieb

Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different…

Computer Vision and Pattern Recognition · Computer Science 2022-11-02 Rey Mendoza , Minh Nguyen , Judith Weng Zhu , Vincent Dumont , Talita Perciano , Juliane Mueller , Vidya Ganapati

The wavelet frame systems have been playing an active role in image restoration and many other image processing fields over the past decades, owing to the good capability of sparsely approximating piece-wise smooth functions such as images.…

Computer Vision and Pattern Recognition · Computer Science 2016-03-29 Liangtian He , Yilun Wang , Zhaoyin Xiang