Publications related to Regularized least squares

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Michaël Unser, Nikolaos Stergiopoulos, Emrah Bostan, Orestis Vardoulis, Stamatios Lefkimmiatis

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Volkan Cevher, Jonathan Mark Scarlett, Yen-Huan Li

We consider the model selection consistency or sparsistency of a broad set of

\ell_1

-regularized

M

-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSS ...

2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

2015

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

Idiap2015

Adaptive regularized diffusion adaptation over multitask networks

Ali H. Sayed, Sadaf Monajemi

The focus of this paper is on multitask learning over adaptive networks where different clusters of nodes have different objectives. We propose an adaptive regularized diffusion strategy using Gaussian kernel regularization to enable the agents to learn ab ...

2015

Towards Convenient Calibration for Cross-Ratio based Gaze Estimation

Jean-Philippe Thiran, Nuri Murat Arar, Hua Gao

Eye gaze movements are considered as a salient modality for human computer interaction applications. Recently, cross-ratio (CR) based eye tracking methods have attracted increasing interest because they provide remote gaze estimation using a single uncalib ...

2015

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Matthieu Martin Jean-André Simeoni

The Square Kilometre Array (SKA) will form the largest radio telescope ever built, generating on the order of one terabyte of data per second. To reduce the data flow sent to the central processor, hierarchical designs have been proposed: the data is prima ...

2015

Quantization Design for Unconstrained Distributed Optimization

Colin Neil Jones, Ye Pu, Melanie Nicole Zeilinger

We consider an unconstrained distributed optimization problem and assume that the bit rate of the communication in the network is limited. We propose a distributed optimization algorithm with an iteratively refining quantization design, which bounds the qu ...

2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

From averaging to acceleration, there is only a step-size

Nicolas Henri Bernard Flammarion

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...

2015

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Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Sparsistency of $\ell_1$-Regularized $M$-Estimators

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Adaptive regularized diffusion adaptation over multitask networks

Towards Convenient Calibration for Cross-Ratio based Gaze Estimation

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Quantization Design for Unconstrained Distributed Optimization

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

From averaging to acceleration, there is only a step-size

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Quantization Design for Unconstrained Distributed Optimization

Towards Convenient Calibration for Cross-Ratio based Gaze Estimation

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Adaptive regularized diffusion adaptation over multitask networks

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

From averaging to acceleration, there is only a step-size