Concept

Radon transform

Related publications (26)

Deep Learning Meets Sparse Regularization

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...

2023

Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

2023

An Inverse-Filter-Based Method to Locate Partial Discharge Sources in Power Transformers

Farhad Rachidi-Haeri, Marcos Rubinstein, Hamidreza Karami

Partial discharge (PD) occurrence in power transformers can lead to irreparable damage to the power network. In this paper, the inverse filter (IF) method to localize PDs in power transformers is proposed. To the best of the authors’ knowledge, this is the ...

2022

Piecewise linear interface-capturing volume-of-fluid method in axisymmetric cylindrical coordinates

Andreas Pautz, Lubomír Bures, Yohei Sato

The paper describes a novel implementation of the piecewise linear interface-capturing volume-of-fluid method (PLIC-VOF) in axisymmetric cylindrical coordinates. The principal innovative feature involved in this work is that both the forward and inverse re ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Methods and apparatus for three-dimensional fabrication by tomographic back projections

Christophe Moser, Paul Delrot, Damien Claude-Marie Loterie

A method for producing a three-dimensional object comprising computing a sequence of back-projections describing the three-dimensional object to be formed from different orientation angles of said object, defining a sequence of patterns of light using said ...

2019

Optical projection tomography for whole organ imaging

David Nguyen

In the past twenty years, far-reaching studies of molecular and cellular processes have reached a milestone in their maturation, and the knowledge from these studies was ready to apply at higher organizational levels. At that time, rodent models were long ...

EPFL2019

Imaging from Echoes: On Inverse Problems in Ultrasound

Adrien Georges Jean Besson

Ultrasound (US) imaging is currently living a revolution. On the one hand, ultrafast US imaging, a novel way of acquiring and producing US images, has paved the way to several advanced imaging modes, e.g. shear-wave elastography, ultrafast Doppler imaging ...

EPFL2018

Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy

Michaël Unser, Emmanuel Emilien Louis Soubies

While structured-illumination microscopy (SIM) is inherently a three-dimensional (3-D) technique, many biological questions can be addressed from the acquisition of a single focal plane with high lateral resolution. Unfortunately, the single-slice reconstr ...

2019

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Kyong Hwan Jin

Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

High-Quality Parallel-Ray x-Ray CT Back Projection Using Optimized Interpolation

Michaël Unser, Michael Thompson McCann

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of para ...

2017

A Versatile Noise Performance Metric for Electrical Impedance Tomography Algorithms

Jean-Philippe Thiran, Fabian Braun, Martin Proença

Electrical impedance tomography (EIT) is an emerging technology for real-time monitoring of patients under mechanical ventilation. EIT has the potential to offer continuous medical monitoring while being noninvasive, radiation free, and low cost. Due to th ...

Ieee-Inst Electrical Electronics Engineers Inc2017

A Forward Regridding Method with Minimal Oversampling for Accurate and Efficient Iterative Tomographic Algorithms

Masih Nilchian, Marco Stampanoni

Reconstruction of underconstrained tomographic data sets remains a major challenge. Standard analytical techniques frequently lead to unsatisfactory results due to insufficient information. Several iterative algorithms, which can easily integrate a priori ...

IEEE2016

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Kyong Hwan Jin

Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter-based low-rank Hankel matrix approach is proposed as a general fr ...

IEEE2016

A Point-Spread-Function-Aware Filtered Backprojection Algorithm for Focal-Plane-Scanning Optical Projection Tomography

Michael Stefan Daniel Liebling

Traditional optical projection tomography requires the use of low numerical aperture objectives in order to achieve a large depth of field and approximate parallel projection geometry. However, low NA objectives suffer from poor resolution, resulting in bl ...

2016

Fast 3D reconstruction method for differential phase contrast X-ray CT

Michaël Unser, Masih Nilchian, Michael Thompson McCann, Marco Stampanoni

We present a fast algorithm for fully 3D regularized X-ray tomography reconstruction for both traditional and differential phase contrast measurements. In many applications, it is critical to reduce the X-ray dose while producing high-quality reconstructio ...

2016

Metal artefact reduction in computed tomography images by a fourth-order total variation flow

Alfio Quarteroni, Elena Faggiano

Permanent metallic implants, such as dental fillings and cardiac devices, generate streaks-like artefacts in computed tomography (CT) images. In this article, we propose a strategy to perform metal artefact reduction (MAR) that relies on the total variatio ...

Taylor & Francis Ltd2016

Global Optimization for Image Restoration in Optical/IR Interferometry

Ferréol Arnaud Marie Soulez

Many image reconstruction algorithms have been proposed to cope with optical/IR interferometric data. A first difficulty is to deal with the sparsity of the data and the uneven u-v coverage. This is usually overcome by imposing a priori constraints to the ...

SPIE2016

An Algorithmic Framework for Mumford-Shah Regularization of Inverse Problems in Imaging

Martin Kurt Storath

The Mumford-Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this pap ...

Iop Publishing Ltd2015

Joint image reconstruction and segmentation using the Potts model

Michaël Unser, Martin Kurt Storath

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficie ...

Institute of Physics2015

Extension of ultrasound Fourier slice Imaging theory to sectorial acquisition

Jean-Philippe Thiran, Rafael Eduardo Carrillo Rangel, Adrien Georges Jean Besson, Olivier Bernard

Ultrasound image reconstruction from the echoes received by an ultrasound probe after the transmission of diverging waves is an active area of research because of its capacity to insonify at ultra-high frame rate with large regions of interest using small ...

2015