# Posts

### ROP inception

Here is a new short preprint: “ROP inception: signal estimation with quadratic random sketching”, available here and on arXiv. This is the first work of Rémi Delogne, carried out in collaboration with Vincent Schellekens and me.

### 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.

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


### 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

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].

### 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 $$w \in \mathbb R^N$$, \[(1-\delta)\|w\|^2\leq \|\Phi w\|^2 \leq (1+\delta)\|w\|^2.

### 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"