Next Article in Journal
Robust Biometric Authentication from an Information Theoretic Perspective
Next Article in Special Issue
Log Likelihood Spectral Distance, Entropy Rate Power, and Mutual Information with Applications to Speech Coding
Previous Article in Journal
Entropy Analysis on Electro-Kinetically Modulated Peristaltic Propulsion of Magnetized Nanofluid Flow through a Microchannel
Previous Article in Special Issue
A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities
Open AccessArticle

A Characterization of the Domain of Beta-Divergence and Its Connection to Bregman Variational Model

School of Liberal Arts, Korea University of Technology and Education, Cheonan 31253, Korea
Entropy 2017, 19(9), 482; https://doi.org/10.3390/e19090482
Received: 20 July 2017 / Revised: 4 September 2017 / Accepted: 7 September 2017 / Published: 9 September 2017
(This article belongs to the Special Issue Entropy in Signal Analysis)
In image and signal processing, the beta-divergence is well known as a similarity measure between two positive objects. However, it is unclear whether or not the distance-like structure of beta-divergence is preserved, if we extend the domain of the beta-divergence to the negative region. In this article, we study the domain of the beta-divergence and its connection to the Bregman-divergence associated with the convex function of Legendre type. In fact, we show that the domain of beta-divergence (and the corresponding Bregman-divergence) include negative region under the mild condition on the beta value. Additionally, through the relation between the beta-divergence and the Bregman-divergence, we can reformulate various variational models appearing in image processing problems into a unified framework, namely the Bregman variational model. This model has a strong advantage compared to the beta-divergence-based model due to the dual structure of the Bregman-divergence. As an example, we demonstrate how we can build up a convex reformulated variational model with a negative domain for the classic nonconvex problem, which usually appears in synthetic aperture radar image processing problems. View Full-Text
Keywords: beta-divergence; bregman-divergence; sparsity; convex function of legendre type; optimization; synthetic aperture radar; multiplicative noise; bregman proximity operator; convexity; total variation beta-divergence; bregman-divergence; sparsity; convex function of legendre type; optimization; synthetic aperture radar; multiplicative noise; bregman proximity operator; convexity; total variation
Show Figures

Figure 1

MDPI and ACS Style

Woo, H. A Characterization of the Domain of Beta-Divergence and Its Connection to Bregman Variational Model. Entropy 2017, 19, 482.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop