Publications related to Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

Fast and robust estimation of NODDI parameters using non-Gaussian noise models and spatial regularization

Jean-Philippe Thiran, Erick Jorge Canales Rodriguez, Alessandro Daducci

In this study, we developed a robust inversion algorithm to estimate the Neurite Orientation Dispersion and Density Imaging (NODDI) model. It is based on the Accelerated Microstructure Imaging via Convex Optimization (AMICO) framework. However, in contrast ...

2018

Phaseless Diffraction Tomography With Regularized Beam Propagation

Michaël Unser, Demetri Psaltis, Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies, Ferréol Arnaud Marie Soulez, Alexandre Goy, Joowon Lim

In recent years, researchers have obtained impressive reconstructions of the refractive index (RI) of biological objects through the combined use of advanced physics (nonlinear forward model) and regularization. Here, we propose an adaptation of these tech ...

IEEE2018

A Fourier dimensionality reduction model for big data interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Vijay Kartik

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging method ...

Oxford Univ Press2017

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

Estimation Error of the Constrained Lasso

Volkan Cevher, Yen-Huan Li, Ya-Ping Hsieh, Nissim Zerbib

This paper presents a non-asymptotic upper bound for the estimation error of the constrained lasso, under the high-dimensional (

n \ll p

) setting. In contrast to existing results, the error bound in this paper is sharp, is valid when the parameter to be e ...

2016

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

Jump-Sparse and Sparse Recovery Using Potts Functionals

Martin Kurt Storath

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and pr ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Model-based Sketching and Recovery with Expanders

Volkan Cevher, Luca Baldassarre, Bubacarr Bah

Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing. This paper conside ...

2014

Sparsity in tensor optimization for optical-interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Anna Auria Rasclosa

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We review our previous work, which reformulates this nonlinear problem in the framework of tensor recover ...

IEEE2014

Geometric Variational Models for Inverse Problems in Imaging

Virginia Estellers Casas

This dissertation develops geometric variational models for different inverse problems in imaging that are ill-posed, designing at the same time efficient numerical algorithms to compute their solutions. Variational methods solve inverse problems by the fo ...

EPFL2013

Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

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Fast and robust estimation of NODDI parameters using non-Gaussian noise models and spatial regularization

Phaseless Diffraction Tomography With Regularized Beam Propagation

A Fourier dimensionality reduction model for big data interferometric imaging

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Estimation Error of the Constrained Lasso

PURIFY: a new approach to radio-interferometric imaging

Jump-Sparse and Sparse Recovery Using Potts Functionals

Model-based Sketching and Recovery with Expanders

Sparsity in tensor optimization for optical-interferometric imaging

Geometric Variational Models for Inverse Problems in Imaging

Phaseless Diffraction Tomography With Regularized Beam Propagation

A Fourier dimensionality reduction model for big data interferometric imaging

Estimation Error of the Constrained Lasso

Geometric Variational Models for Inverse Problems in Imaging

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Jump-Sparse and Sparse Recovery Using Potts Functionals

Sparsity in tensor optimization for optical-interferometric imaging

PURIFY: a new approach to radio-interferometric imaging

Model-based Sketching and Recovery with Expanders

Fast and robust estimation of NODDI parameters using non-Gaussian noise models and spatial regularization