232,521 research outputs found
Manifold Graph Signal Restoration using Gradient Graph Laplacian Regularizer
In the graph signal processing (GSP) literature, graph Laplacian regularizer
(GLR) was used for signal restoration to promote piecewise smooth / constant
reconstruction with respect to an underlying graph. However, for signals slowly
varying across graph kernels, GLR suffers from an undesirable "staircase"
effect. In this paper, focusing on manifold graphs -- collections of uniform
discrete samples on low-dimensional continuous manifolds -- we generalize GLR
to gradient graph Laplacian regularizer (GGLR) that promotes planar / piecewise
planar (PWP) signal reconstruction. Specifically, for a graph endowed with
sampling coordinates (e.g., 2D images, 3D point clouds), we first define a
gradient operator, using which we construct a gradient graph for nodes'
gradients in sampling manifold space. This maps to a gradient-induced nodal
graph (GNG) and a positive semi-definite (PSD) Laplacian matrix with planar
signals as the 0 frequencies. For manifold graphs without explicit sampling
coordinates, we propose a graph embedding method to obtain node coordinates via
fast eigenvector computation. We derive the means-square-error minimizing
weight parameter for GGLR efficiently, trading off bias and variance of the
signal estimate. Experimental results show that GGLR outperformed previous
graph signal priors like GLR and graph total variation (GTV) in a range of
graph signal restoration tasks
Massive MIMO for Crowd Scenarios: A Solution Based on Random Access
This paper presents a new approach to intra-cell pilot contamination in
crowded massive MIMO scenarios. The approach relies on two essential properties
of a massive MIMO system, namely near-orthogonality between user channels and
near-stability of channel powers. Signal processing techniques that take
advantage of these properties allow us to view a set of contaminated pilot
signals as a graph code on which iterative belief propagation can be performed.
This makes it possible to decontaminate pilot signals and increase the
throughput of the system. The proposed solution exhibits high performance with
large improvements over the conventional method. The improvements come at the
price of an increased error rate, although this effect is shown to decrease
significantly for increasing number of antennas at the base station
Active Semi-Supervised Learning Using Sampling Theory for Graph Signals
We consider the problem of offline, pool-based active semi-supervised
learning on graphs. This problem is important when the labeled data is scarce
and expensive whereas unlabeled data is easily available. The data points are
represented by the vertices of an undirected graph with the similarity between
them captured by the edge weights. Given a target number of nodes to label, the
goal is to choose those nodes that are most informative and then predict the
unknown labels. We propose a novel framework for this problem based on our
recent results on sampling theory for graph signals. A graph signal is a
real-valued function defined on each node of the graph. A notion of frequency
for such signals can be defined using the spectrum of the graph Laplacian
matrix. The sampling theory for graph signals aims to extend the traditional
Nyquist-Shannon sampling theory by allowing us to identify the class of graph
signals that can be reconstructed from their values on a subset of vertices.
This approach allows us to define a criterion for active learning based on
sampling set selection which aims at maximizing the frequency of the signals
that can be reconstructed from their samples on the set. Experiments show the
effectiveness of our method.Comment: 10 pages, 6 figures, To appear in KDD'1
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