dithering

Small Width, Low Distortions: Quantized Random Embeddings of Low-complexity Sets

Abstract: Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a finite set of vectors?

The Rare Eclipse Problem on Tiles: Quantised Embeddings of Disjoint Convex Sets

Abstract: Quantised random embeddings are an efficient dimensionality reduction technique which preserves the distances of low-complexity signals up to some controllable additive and multiplicative distortions. In this work, we instead focus on verifying when this technique preserves the separability of two disjoint closed convex sets, i.

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.