6,095 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
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
We address the denoising of images contaminated with multiplicative noise,
e.g. speckle noise. Classical ways to solve such problems are filtering,
statistical (Bayesian) methods, variational methods, and methods that convert
the multiplicative noise into additive noise (using a logarithmic function),
shrinkage of the coefficients of the log-image data in a wavelet basis or in a
frame, and transform back the result using an exponential function. We propose
a method composed of several stages: we use the log-image data and apply a
reasonable under-optimal hard-thresholding on its curvelet transform; then we
apply a variational method where we minimize a specialized criterion composed
of an data-fitting to the thresholded coefficients and a Total
Variation regularization (TV) term in the image domain; the restored image is
an exponential of the obtained minimizer, weighted in a way that the mean of
the original image is preserved. Our restored images combine the advantages of
shrinkage and variational methods and avoid their main drawbacks. For the
minimization stage, we propose a properly adapted fast minimization scheme
based on Douglas-Rachford splitting. The existence of a minimizer of our
specialized criterion being proven, we demonstrate the convergence of the
minimization scheme. The obtained numerical results outperform the main
alternative methods
Distributed Big-Data Optimization via Block Communications
We study distributed multi-agent large-scale optimization problems, wherein
the cost function is composed of a smooth possibly nonconvex sum-utility plus a
DC (Difference-of-Convex) regularizer. We consider the scenario where the
dimension of the optimization variables is so large that optimizing and/or
transmitting the entire set of variables could cause unaffordable computation
and communication overhead. To address this issue, we propose the first
distributed algorithm whereby agents optimize and communicate only a portion of
their local variables. The scheme hinges on successive convex approximation
(SCA) to handle the nonconvexity of the objective function, coupled with a
novel block-signal tracking scheme, aiming at locally estimating the average of
the agents' gradients. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Numerical results on a sparse regression
problem show the effectiveness of the proposed algorithm and the impact of the
block size on its practical convergence speed and communication cost
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
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