94,151 research outputs found
Convexity in source separation: Models, geometry, and algorithms
Source separation or demixing is the process of extracting multiple
components entangled within a signal. Contemporary signal processing presents a
host of difficult source separation problems, from interference cancellation to
background subtraction, blind deconvolution, and even dictionary learning.
Despite the recent progress in each of these applications, advances in
high-throughput sensor technology place demixing algorithms under pressure to
accommodate extremely high-dimensional signals, separate an ever larger number
of sources, and cope with more sophisticated signal and mixing models. These
difficulties are exacerbated by the need for real-time action in automated
decision-making systems.
Recent advances in convex optimization provide a simple framework for
efficiently solving numerous difficult demixing problems. This article provides
an overview of the emerging field, explains the theory that governs the
underlying procedures, and surveys algorithms that solve them efficiently. We
aim to equip practitioners with a toolkit for constructing their own demixing
algorithms that work, as well as concrete intuition for why they work
Generalized Bregman Divergence and Gradient of Mutual Information for Vector Poisson Channels
We investigate connections between information-theoretic and
estimation-theoretic quantities in vector Poisson channel models. In
particular, we generalize the gradient of mutual information with respect to
key system parameters from the scalar to the vector Poisson channel model. We
also propose, as another contribution, a generalization of the classical
Bregman divergence that offers a means to encapsulate under a unifying
framework the gradient of mutual information results for scalar and vector
Poisson and Gaussian channel models. The so-called generalized Bregman
divergence is also shown to exhibit various properties akin to the properties
of the classical version. The vector Poisson channel model is drawing
considerable attention in view of its application in various domains: as an
example, the availability of the gradient of mutual information can be used in
conjunction with gradient descent methods to effect compressive-sensing
projection designs in emerging X-ray and document classification applications
A Unifying Variational Perspective on Some Fundamental Information Theoretic Inequalities
This paper proposes a unifying variational approach for proving and extending
some fundamental information theoretic inequalities. Fundamental information
theory results such as maximization of differential entropy, minimization of
Fisher information (Cram\'er-Rao inequality), worst additive noise lemma,
entropy power inequality (EPI), and extremal entropy inequality (EEI) are
interpreted as functional problems and proved within the framework of calculus
of variations. Several applications and possible extensions of the proposed
results are briefly mentioned
A complete closed-form solution to a tropical extremal problem
A multidimensional extremal problem in the idempotent algebra setting is
considered which consists in minimizing a nonlinear functional defined on a
finite-dimensional semimodule over an idempotent semifield. The problem
integrates two other known problems by combining their objective functions into
one general function and includes these problems as particular cases. A new
solution approach is proposed based on the analysis of linear inequalities and
spectral properties of matrices. The approach offers a comprehensive solution
to the problem in a closed form that involves performing simple matrix and
vector operations in terms of idempotent algebra and provides a basis for the
development of efficient computational algorithms and their software
implementation.Comment: Proceedings of the 6th WSEAS European Computing Conference (ECC '12),
Prague, Czech Republic, September 24-26, 201
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