We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is stable with respect to the specified noise model; we call the resulting procedure a stable autoencoder. In the simplest case, with an isotropic ...

Bayesian filtering appears in many signal processing problems, reason why it attracted the attention of many researchers to develop efficient algorithms, yet computationally affordable. In many real systems, it is appropriate to consider α–stable noise distributions to model possible outliers or impulsive behavior in the measurements. In this paper, we consider a nonlinear state–space model wit...

We study the effects of noise on the Lorenz equations in the parameter regime admitting two stable fixed point solutions and a strange attractor. We show that noise annihilates the two stable fixed point attractors and evicts a Hopf-bifurcation-like sequence and transition to chaos. The noise-induced oscillatory motions have very well defined period and amplitude, and this phenomenon is similar...

Impulsive noise arises in many communication systems—ranging from wireless to molecular—and is often modeled via the α-stable distribution. In this paper, we investigate properties of the capacity of complex isotropic α-stable noise channels, which can arise in the context of wireless cellular communications and are not well understood at present. In particular, we derive a tractable lower boun...

The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...

In this paper we propose an on-line Bayesian filtering and smoothing method for time series models with heavy-tailed α-stable noise, with a particular focus on TVAR models. α-stable processes have been shown in the past to be a good model for many naturally occurring noise sources, see e.g. [1, 2]. We first point out how a filter that fails to take into account the heavy-tailed character of the...