Publications related to An Efficient Numerical Method for General

A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomoge ...

Institute of Physics2017

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

EPFL2016

Graph Based Sinogram Denoising for Tomographic Reconstructions

Pierre Vandergheynst, Nauman Shahid

Limited data and low dose constraints are common problems in a variety of tomographic reconstruction paradigms which lead to noisy and incomplete data. Over the past few years sinogram denoising has become an essential pre-processing step for low dose Comp ...

2016

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

PURIFY: a new approach to radio-interferometric imaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a m ...

Wiley-Blackwell2014

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Michaël Unser, Cédric René Jean Vonesch, Peter Modregger, Masih Nilchian, Marco Stampanoni

X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed ...

IEEE2013

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

On Sparsity Averaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

Recent developments in [1] and [2] introduced a novel regularization method for compressive imaging in the con- text of compressed sensing with coherent redundant dictionaries. The approach relies on the observation that natural images exhibit strong avera ...

2013

A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

Michaël Unser, Christian Depeursinge, Nicolas Pavillon, Emrah Bostan, Aurélien Bourquard

In this paper, we propose a new technique for high-quality reconstruction from single digital holographic acquisitions. The unknown complex object field is found as the solution of a nonlinear inverse problem that consists in the minimization of an energy ...

OSA2013

An Efficient Numerical Method for General

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A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Graph Based Sinogram Denoising for Tomographic Reconstructions

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

PURIFY: a new approach to radio-interferometric imaging

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

On Sparsity Averaging

A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

PURIFY: a new approach to radio-interferometric imaging

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

Graph Based Sinogram Denoising for Tomographic Reconstructions

On Sparsity Averaging

A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms