# General

### 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.

### 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.

### 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.

### 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.[/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.

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

Last July, I read the biography of Paul Erdős written by Paul Hoffman and entitled “The Man Who Loved Only Numbers”. This is really a wonderful book sprinkled with many anecdotes about the particular life of this great mathematician and about his appealing mathematical obsessions (including prime numbers).

### 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].

### 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 $w\in \mathbb R^N$,