Related papers: Bounds on restricted isometry constants of random …
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
This paper studies the stability of some reconstruction algorithms for compressed sensing in terms of the bit precision. Considering the fact that practical digital systems deal with discretized signals, we motivate the importance of the…
We prove generalised concentration inequalities for a class of scaled self-bounding functions of independent random variables, referred to as ${(M,a,b)}$ self-bounding. The scaling refers to the fact that the component-wise difference is…
Pushing the boundaries of measurement precision is central for sensing and metrology, pursued by nonclassical resources such as squeezing, and non-Hermitian degeneracies with distinct spectral response. Their convergence, however, remains…
Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using…
Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under…
Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
Multivariate tempered stable random measures (ISRMs) are constructed and their corresponding space of integrable functions is characterized in terms of a quasi-norm utilizing the so-called Rosinski measure of a tempered stable law. In the…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Compressed sensing is an image reconstruction technique to achieve high-quality results from limited amount of data. In order to achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. Focusing on image…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
Quadratically-constrained basis pursuit has become a popular device in sparse regularization; in particular, in the context of compressed sensing. However, the majority of theoretical error estimates for this regularizer assume an a priori…
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…