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.

I have always been intrigued by the fact that, in Compressed Sensing (CS), beyond Gaussian random matrices, a couple of other unstructured random matrices respecting, with high probability (whp), the Restricted Isometry Property (RIP) look like “quantized” version of the Gaussian case, i.

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.

It took me a certain time to do it. Here is at least a first attempt to test numerically the validity of some of the results I obtained in “A Quantized Johnson Lindenstrauss Lemma: The Finding of Buffon’s Needle” (arXiv) I have decided to avoid using the too conventional matlab environment.

Quasi-isometric embeddings of vector sets with quantized sub-Gaussian projections | Le Petit Chercheur Illustré - Apr 2, 2015
[…] explained in my previous post on quantized embedding and the funny connection with Buffon’s needle problem, I have recently noticed that for finite […]

[caption id=“attachment_346” align=“alignnone” width=“640”] (left) Picture of [8, page 147] stating the initial formulation of Buffon’s needle problem (Courtesy of E. Kowalski’s blog) (right) Scheme of Buffon’s needle problem.[/caption](This post is related to a paper entitled “A Quantized Johnson Lindenstrauss Lemma: The Finding of Buffon’s Needle” (arxiv, pdf) that I have recently submitted for publication.

Last Thursday after an email discussion with Thomas Arildsen, I was thinking again to the nice embedding properties discovered by Y. Plan and R. Vershynin in the context of 1-bit compressed sensing (CS) [1].

Recently, for some unrelated reasons, I discovered that it is actually very easy to generate a Gaussian matrix $ \Phi$ that does not respect the restricted isometry property (RIP) [1]. I recall that such a matrix is RIP if there exists a (restricted isometry) constant $ 0<\delta<1$ such that, for any $ K$-sparse vector $ w\in \mathbb R^N$,

Laurent Duval - Dec 5, 2011
16 month is quite short when you compare to cosmic times

I have just found this “new” (well 150 years old actually) tomographical method… for measuring the magnetic field of our own galaxy
“New all-sky map shows the magnetic fields of the Milky Way with the highest precision”