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 There is time for dithering in a quantized world of reduced dimensionality!
 Quantized subGaussian random matrices are still RIP!
 Quasiisometric embeddings of vector sets with quantized subGaussian projections
 Testing a QuasiIsometric Quantized Embedding
 When Buffon’s needle problem meets the JohnsonLindenstrauss Lemma
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Author Archives: jackdurden
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 lowcomplexity vectors, such as the set of sparse (or compressible) signals in a certain basis/dictionary, the set of lowrank matrices … Continue reading
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Quantized subGaussian 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 … Continue reading
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Quasiisometric embeddings of vector sets with quantized subGaussian 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 … Continue reading
Testing a QuasiIsometric 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 … Continue reading
When Buffon’s needle problem meets the JohnsonLindenstrauss Lemma
(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 July, I read the biography of Paul Erdős written by Paul Hoffman … Continue reading
Posted in Compressed Sensing, General, Johnson Lindenstrauss
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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 1bit compressed sensing (CS) [1]. I was wondering if these could … Continue reading
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A useless nonRIP Gaussian matrix
Recently, for some unrelated reasons, I discovered that it is actually very easy to generate a Gaussian matrix that does not respect the restricted isometry property (RIP) [1]. I recall that such a matrix is RIP if there exists a … Continue reading
Posted in Compressed Sensing, General
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