Lpcis

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 sub-Gaussian random matrices are still RIP!

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.

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.

Testing a Quasi-Isometric Quantized Embedding

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.

When Buffon's needle problem meets the Johnson-Lindenstrauss Lemma

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 […]

When Buffon's needle problem meets the Johnson-Lindenstrauss Lemma

[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.

Recovering sparse signals from sparsely corrupted compressed measurements

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].

A useless non-RIP Gaussian matrix

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$,

Tomography of the magnetic fields of the Milky Way?

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

Tomography of the magnetic fields of the Milky Way?

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”