5,608 research outputs found
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
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
Convolutional Neural Networks Via Node-Varying Graph Filters
Convolutional neural networks (CNNs) are being applied to an increasing
number of problems and fields due to their superior performance in
classification and regression tasks. Since two of the key operations that CNNs
implement are convolution and pooling, this type of networks is implicitly
designed to act on data described by regular structures such as images.
Motivated by the recent interest in processing signals defined in irregular
domains, we advocate a CNN architecture that operates on signals supported on
graphs. The proposed design replaces the classical convolution not with a
node-invariant graph filter (GF), which is the natural generalization of
convolution to graph domains, but with a node-varying GF. This filter extracts
different local features without increasing the output dimension of each layer
and, as a result, bypasses the need for a pooling stage while involving only
local operations. A second contribution is to replace the node-varying GF with
a hybrid node-varying GF, which is a new type of GF introduced in this paper.
While the alternative architecture can still be run locally without requiring a
pooling stage, the number of trainable parameters is smaller and can be
rendered independent of the data dimension. Tests are run on a synthetic source
localization problem and on the 20NEWS dataset.Comment: Submitted to DSW 2018 (IEEE Data Science Workshop
Spectral Graph Convolutions for Population-based Disease Prediction
Exploiting the wealth of imaging and non-imaging information for disease
prediction tasks requires models capable of representing, at the same time,
individual features as well as data associations between subjects from
potentially large populations. Graphs provide a natural framework for such
tasks, yet previous graph-based approaches focus on pairwise similarities
without modelling the subjects' individual characteristics and features. On the
other hand, relying solely on subject-specific imaging feature vectors fails to
model the interaction and similarity between subjects, which can reduce
performance. In this paper, we introduce the novel concept of Graph
Convolutional Networks (GCN) for brain analysis in populations, combining
imaging and non-imaging data. We represent populations as a sparse graph where
its vertices are associated with image-based feature vectors and the edges
encode phenotypic information. This structure was used to train a GCN model on
partially labelled graphs, aiming to infer the classes of unlabelled nodes from
the node features and pairwise associations between subjects. We demonstrate
the potential of the method on the challenging ADNI and ABIDE databases, as a
proof of concept of the benefit from integrating contextual information in
classification tasks. This has a clear impact on the quality of the
predictions, leading to 69.5% accuracy for ABIDE (outperforming the current
state of the art of 66.8%) and 77% for ADNI for prediction of MCI conversion,
significantly outperforming standard linear classifiers where only individual
features are considered.Comment: International Conference on Medical Image Computing and
Computer-Assisted Interventions (MICCAI) 201
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