Blind Signal Separation in the Presence of Gaussian Noise

by   Mikhail Belkin, et al.

A prototypical blind signal separation problem is the so-called cocktail party problem, with n people talking simultaneously and n different microphones within a room. The goal is to recover each speech signal from the microphone inputs. Mathematically this can be modeled by assuming that we are given samples from an n-dimensional random variable X=AS, where S is a vector whose coordinates are independent random variables corresponding to each speaker. The objective is to recover the matrix A^-1 given random samples from X. A range of techniques collectively known as Independent Component Analysis (ICA) have been proposed to address this problem in the signal processing and machine learning literature. Many of these techniques are based on using the kurtosis or other cumulants to recover the components. In this paper we propose a new algorithm for solving the blind signal separation problem in the presence of additive Gaussian noise, when we are given samples from X=AS+η, where η is drawn from an unknown, not necessarily spherical n-dimensional Gaussian distribution. Our approach is based on a method for decorrelating a sample with additive Gaussian noise under the assumption that the underlying distribution is a linear transformation of a distribution with independent components. Our decorrelation routine is based on the properties of cumulant tensors and can be combined with any standard cumulant-based method for ICA to get an algorithm that is provably robust in the presence of Gaussian noise. We derive polynomial bounds for the sample complexity and error propagation of our method.


page 1

page 2

page 3

page 4


Sparse Gaussian ICA

Independent component analysis (ICA) is a cornerstone of modern data ana...

A Pseudo-Euclidean Iteration for Optimal Recovery in Noisy ICA

Independent Component Analysis (ICA) is a popular model for blind signal...

Algorithms for Learning Sparse Additive Models with Interactions in High Dimensions

A function f: R^d →R is a Sparse Additive Model (SPAM), if it is of the ...

Data blurring: sample splitting a single sample

Suppose we observe a random vector X from some distribution P in a known...

Sample Complexity Bounds for Learning High-dimensional Simplices in Noisy Regimes

In this paper, we propose a sample complexity bound for learning a simpl...

A New Noise-Assistant LMS Algorithm for Preventing the Stalling Effect

In this paper, we introduce a new algorithm to deal with the stalling ef...

Statistical Analysis of Signal-Dependent Noise: Application in Blind Localization of Image Splicing Forgery

Visual noise is often regarded as a disturbance in image quality, wherea...

Please sign up or login with your details

Forgot password? Click here to reset