Publications related to Convex Optimization for Big Data

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

Designing Gabor windows using convex optimization

Nathanaël Perraudin

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l(2)-norm dual window, is widely used. This window function however, might lack desirable properties, e. g. good time-fre ...

ELSEVIER SCIENCE INC2018

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

Volkan Cevher, Anastasios Kyrillidis, Ya-Ping Hsieh, Rabeeh Karimi Mahabadi, Yu-Chun Kao

We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity as well as faster convergence speed. Moreover, many of ...

2018

A Data-Driven Approach to Power Converter Control via Convex Optimization

Alireza Karimi, Achille Nicoletti, Michele Martino

A new model reference data-driven approach is presented for synthesizing controllers for the CERN power converter control system. This method uses the frequency re- sponse function (FRF) of a system in order to avoid the problem of unmodeled dynamics assoc ...

2017

Combinatorial Penalties: Which structures are preserved by convex relaxations?

Volkan Cevher, Marwa El Halabi

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinato ...

2017

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

Stochastic Three-Composite Convex Minimization

Volkan Cevher, Alp Yurtsever, Cong Bang Vu

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computati ...

2016

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

Volkan Cevher

This paper proposes a tradeoff between computational time, sample complexity, and statistical accuracy that applies to statistical estimators based on convex optimization. When we have a large amount of data, we can exploit excess samples to decrease stati ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Why CLEAN when you can PURIFY? A new approach for next-generation radio-interferometric imaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

In recent works, sparse models and convex optimization techniques have been applied to radio-interferometric (RI) imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. In this talk, I will review our latest contribut ...

2015

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

Alireza Karimi, Achille Nicoletti, Zlatko Emedi

In this paper, a new method for designing robust fixed-order

\mathcal{H}_{\infty}

discrete-time controllers is presented. The controller structure is a two-degree of freedom polynomial controller of the

RST

type. A data-driven approach is implemented f ...

IEEE2015

Convex Optimization for Big Data

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

Designing Gabor windows using convex optimization

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

A Data-Driven Approach to Power Converter Control via Convex Optimization

Combinatorial Penalties: Which structures are preserved by convex relaxations?

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

Stochastic Three-Composite Convex Minimization

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

Why CLEAN when you can PURIFY? A new approach for next-generation radio-interferometric imaging

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

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

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

Designing Gabor windows using convex optimization

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

Stochastic Three-Composite Convex Minimization

A Data-Driven Approach to Power Converter Control via Convex Optimization

Why CLEAN when you can PURIFY? A new approach for next-generation radio-interferometric imaging

A Data-Driven Approach in Designing RST Controllers with H∞ Performance via Convex Optimization

Combinatorial Penalties: Which structures are preserved by convex relaxations?