3,936 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs
We address the problem of estimating a random vector X from two sets of
measurements Y and Z, such that the estimator is linear in Y. We show that the
partially linear minimum mean squared error (PLMMSE) estimator does not require
knowing the joint distribution of X and Y in full, but rather only its
second-order moments. This renders it of potential interest in various
applications. We further show that the PLMMSE method is minimax-optimal among
all estimators that solely depend on the second-order statistics of X and Y. We
demonstrate our approach in the context of recovering a signal, which is sparse
in a unitary dictionary, from noisy observations of it and of a filtered
version of it. We show that in this setting PLMMSE estimation has a clear
computational advantage, while its performance is comparable to
state-of-the-art algorithms. We apply our approach both in static and dynamic
estimation applications. In the former category, we treat the problem of image
enhancement from blurred/noisy image pairs, where we show that PLMMSE
estimation performs only slightly worse than state-of-the art algorithms, while
running an order of magnitude faster. In the dynamic setting, we provide a
recursive implementation of the estimator and demonstrate its utility in the
context of tracking maneuvering targets from position and acceleration
measurements.Comment: 13 pages, 5 figure
A variational Bayesian method for inverse problems with impulsive noise
We propose a novel numerical method for solving inverse problems subject to
impulsive noises which possibly contain a large number of outliers. The
approach is of Bayesian type, and it exploits a heavy-tailed t distribution for
data noise to achieve robustness with respect to outliers. A hierarchical model
with all hyper-parameters automatically determined from the given data is
described. An algorithm of variational type by minimizing the Kullback-Leibler
divergence between the true posteriori distribution and a separable
approximation is developed. The numerical method is illustrated on several one-
and two-dimensional linear and nonlinear inverse problems arising from heat
conduction, including estimating boundary temperature, heat flux and heat
transfer coefficient. The results show its robustness to outliers and the fast
and steady convergence of the algorithm.Comment: 20 pages, to appear in J. Comput. Phy
- …