24,846 research outputs found
Accelerated graph-based spectral polynomial filters
Graph-based spectral denoising is a low-pass filtering using the
eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial
filtering avoids costly computation of the eigendecomposition by projections
onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the
bilateral and guided filters. We propose constructing accelerated polynomial
filters by running flexible Krylov subspace based linear and eigenvalue solvers
such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG)
method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop
on Machine Learning for Signal Processin
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
Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space
This paper focuses on devising graph signal processing tools for the
treatment of data defined on the edges of a graph. We first show that
conventional tools from graph signal processing may not be suitable for the
analysis of such signals. More specifically, we discuss how the underlying
notion of a `smooth signal' inherited from (the typically considered variants
of) the graph Laplacian are not suitable when dealing with edge signals that
encode a notion of flow. To overcome this limitation we introduce a class of
filters based on the Edge-Laplacian, a special case of the Hodge-Laplacian for
simplicial complexes of order one. We demonstrate how this Edge-Laplacian leads
to low-pass filters that enforce (approximate) flow-conservation in the
processed signals. Moreover, we show how these new filters can be combined with
more classical Laplacian-based processing methods on the line-graph. Finally,
we illustrate the developed tools by denoising synthetic traffic flows on the
London street network.Comment: 5 pages, 2 figur
Weighted Mean Curvature
In image processing tasks, spatial priors are essential for robust
computations, regularization, algorithmic design and Bayesian inference. In
this paper, we introduce weighted mean curvature (WMC) as a novel image prior
and present an efficient computation scheme for its discretization in practical
image processing applications. We first demonstrate the favorable properties of
WMC, such as sampling invariance, scale invariance, and contrast invariance
with Gaussian noise model; and we show the relation of WMC to area
regularization. We further propose an efficient computation scheme for
discretized WMC, which is demonstrated herein to process over 33.2
giga-pixels/second on GPU. This scheme yields itself to a convolutional neural
network representation. Finally, WMC is evaluated on synthetic and real images,
showing its superiority quantitatively to total-variation and mean curvature.Comment: 12 page
Bilateral Filter: Graph Spectral Interpretation and Extensions
In this paper we study the bilateral filter proposed by Tomasi and Manduchi,
as a spectral domain transform defined on a weighted graph. The nodes of this
graph represent the pixels in the image and a graph signal defined on the nodes
represents the intensity values. Edge weights in the graph correspond to the
bilateral filter coefficients and hence are data adaptive. Spectrum of a graph
is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian
matrix. We use this spectral interpretation to generalize the bilateral filter
and propose more flexible and application specific spectral designs of
bilateral-like filters. We show that these spectral filters can be implemented
with k-iterative bilateral filtering operations and do not require expensive
diagonalization of the Laplacian matrix
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