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Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices

Publications associées (81)

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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 ...

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Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the`1-norm. However, several important learning applications cannot benet from this approach as they feature these convex no ...

JMLR W&CP2013

Sparse Distributed Learning Based on Diffusion Adaptation

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This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to enhance the d ...

IEEE2013

Energy-aware adaptive bi-Lipschitz embeddings

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We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as muc ...

2013

Enhanced Compressed Sensing Recovery with Level Set Normals

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We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal vectors of the i ...

2013

On Generalized Weighted Hilbert Matrices

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We study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, the determinant, and various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic ...

Pacific Journal Mathematics2013

Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices

Pierre Vandergheynst, Mohammad Golbabaee

In this paper we consider recovery of a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model which can efficiently restricts the degrees of freedom of data and, at the same time, is generic so that f ...

2012

Nonlinear data description with Principal Polynomial Analysis

Devis Tuia

Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold lear ...

2012

-Hyperspectral Image Compressed Sensing Via Low-Rank And Joint-Sparse Matrix Recovery

Pierre Vandergheynst, Mohammad Golbabaee

We propose a novel approach to reconstruct Hyperspectral images from very few number of noisy compressive measurements. Our reconstruction approach is based on a convex minimization which penalizes both the nuclear norm and the l(2,1) mixed-norm of the dat ...

Ieee2012

Structural Analysis of Network Traffic Matrix via Relaxed Principal Component Pursuit

Xiaowen Dong, Zhe Wang, Ke Xu

The network traffic matrix is widely used in network operation and management. It is of crucial importance to analyze the composition and the structure of the network traffic matrix, for which some mathematical approaches such as Principal Component Analys ...

2012