The Rare Eclipse Problem on Tiles: Quantized Embeddings of Disjoint Convex Sets

(joint work with V. Cambareri and C. Xu). See also arXiv:1702.04664 for the corresponding preprint.

Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets

Abstract: Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors?

The Rare Eclipse Problem on Tiles: Quantised Embeddings of Disjoint Convex Sets

Abstract: Quantised random embeddings are an efficient dimensionality reduction technique which preserves the distances of low-complexity signals up to some controllable additive and multiplicative distortions. In this work, we instead focus on verifying when this technique preserves the separability of two disjoint closed convex sets, i.

Time for dithering: fast and quantized random embeddings via the restricted isometry property

Abstract: Recently, many works have focused on the characterization of non-linear dimensionality reduction methods obtained by quantizing linear embeddings, e.g., to reach fast processing time, efficient data compression procedures, novel geometry-preserving embeddings or to estimate the information/bits stored in this reduced data representation.

There is time for dithering in a quantized world of reduced dimensionality!

I’m glad to announce here a new work made in collaboration with Valerio Cambareri (UCL, Belgium) on quantized embeddings of low-complexity vectors, such as the set of sparse (or compressible) signals in a certain basis/dictionary, the set of low-rank matrices or vectors living in (a union of) subspaces.

Quantized random projections of low-complexity sets

2016 Invited speaker, talk on “”.

Sparse Support Recovery with $ell_{infty}$ Data Fidelity

Abstract: This paper investigates non-uniform guarantees of \(ell_1\) minimization, subject to an \(ell_infty\) data fidelity constraint, to stably recover the support of a sparse vector when solving noisy linear inverse problems.

Quasi-isometric embeddings of vector sets with quantized sub-Gaussian projections

Last January, I was honored to be invited in RWTH Aachen University by Holger Rauhut and Sjoerd Dirksen to give a talk on the general topic of quantized compressed sensing. In particular, I decided to focus my presentation on the quasi-isometric embeddings arising in 1-bit compressed sensing, as developed by a few researchers in this field (e.