Quantized compressive sampling for structured signal estimation

This thesis investigates different approaches to enable the use of compressed sensing (CS)-based acquisition devices in resource-constrained environments relying on cheap, energy-efficient sensors. We consider the acquisition of structured low-complexity signals from excessively quantized 1-bit observations, as well as partial compressive measurements collected by one or multiple sensors. In both scenarios, the central goal is to alleviate the complexity of sensing devices in order to enable signal acquisition by simple, inexpensive sensors. In the first part of the thesis, we address the reconstruction of signals with a sparse Fourier transform from 1-bit time domain measurements. We propose a modification of the binary iterative hard thresholding algorithm, which accounts for the conjugate symmetric structure of the underlying signal space. In this context, a modification of the hard thresholding operator is developed, whose use extends to various other (quantized) CS recovery algorithms. In addition to undersampled measurements, we also consider oversampled signal representations, in which case the measurement operator is deterministic rather than constructed randomly. Numerical experiments verify the correct behavior of the proposed methods. The remainder of the thesis focuses on the reconstruction of group-sparse signals, a signal class in which nonzero components are assumed to appear in nonoverlapping coefficient groups. We first focus on 1-bit quantized Gaussian observations and derive theoretical guarantees for several reconstruction schemes to recover target vectors with a desired level of accuracy. We also address recovery based on dithered quantized observations to resolve the scale ambiguity inherent in the 1-bit CS model to allow for the recovery of both direction and magnitude of group-sparse vectors. In the last part, the acquisition of group-sparse vectors by a collection of independent sensors, which each observe a different portion of a target vector, is considered. Generalizing earlier results for the canonical sparsity model, a bound on the number of measurements required to allow for stable and robust signal recovery is established. The proof relies on a powerful concentration bound on the suprema of chaos processes. In order to establish our main result, we develop an extension of Maurey’s empirical method to bound the covering number of sets which can be represented as convex combinations of elements in compact convex sets

pymanopt/pymanopt: 2.2.0

What's Changed Re-enable build of stable docs by @nkoep in https://github.com/pymanopt/pymanopt/pull/228 Add JAX backend by @nkoep in https://github.com/pymanopt/pymanopt/pull/206 Add utility function to check Hessian operators by @nkoep in https://github.com/pymanopt/pymanopt/pull/230 Migrate from versioneer to setuptools-scm by @nkoep in https://github.com/pymanopt/pymanopt/pull/231 Add unitary group manifold by @nkoep in https://github.com/pymanopt/pymanopt/pull/232 and https://github.com/pymanopt/pymanopt/pull/233 chore: move metadata to pyproject.toml by @SauravMaheshkar in https://github.com/pymanopt/pymanopt/pull/236 Update zenodo to DOI umbrella badge by @nkoep in https://github.com/pymanopt/pymanopt/pull/238 feat(ci): add pip cache to CI by @SauravMaheshkar in https://github.com/pymanopt/pymanopt/pull/239 Add Complex valued manifolds by @antoinecollas in https://github.com/pymanopt/pymanopt/pull/125 New Contributors @SauravMaheshkar made their first contribution in https://github.com/pymanopt/pymanopt/pull/222 Full Changelog: https://github.com/pymanopt/pymanopt/compare/2.1.1...2.2.

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at http://geomstats.ai.Idex UCA JEDI3IA Côte d'AzurG-Statistics - Foundations of Geometric Statistics and Their Application in the Life Science