Signal structure: from manifolds to molecules and structured sparsity
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In this work package (WP), we investigate the possibility of discovering structure within dictionary learning. This could range from exploring groups of atoms that appear in clusters - a form of molecule learning - to learning graphical dependencies across ...
Conventional linear subspace learning methods like principal component analysis (PCA), linear discriminant analysis (LDA) derive subspaces from the whole data set. These approaches have limitations in the sense that they are linear while the data distribut ...
Institute of Electrical and Electronics Engineers2011
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold’s structure. For this purp ...
We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a well-known memory ...
The goal of this paper is to propose diffusion LMS techniques for distributed estimation over adaptive networks, which are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, ...
The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the ℓ2-data error objective and the ℓ1-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection ...
We investigate the strong-coupling regime of a linear x-x coupled harmonic-oscillator system by performing a direct diagonalization of the Hamiltonian. It is shown that the x-x coupled Hamiltonian can be equivalently described by a Mach-Zehnder-type interf ...
We address the problem of building a manifold in order to represent a set of geometrically transformed images by selecting a good common sparse approximation of them with parametric atoms. We propose a greedy method to construct a representative pattern su ...
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a vanishing fraction ...
Institute of Electrical and Electronics Engineers2012
This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...
