676 research outputs found
Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
Over the last decade, kernel methods for nonlinear processing have
successfully been used in the machine learning community. The primary
mathematical tool employed in these methods is the notion of the Reproducing
Kernel Hilbert Space. However, so far, the emphasis has been on batch
techniques. It is only recently, that online techniques have been considered in
the context of adaptive signal processing tasks. Moreover, these efforts have
only been focussed on real valued data sequences. To the best of our knowledge,
no adaptive kernel-based strategy has been developed, so far, for complex
valued signals. Furthermore, although the real reproducing kernels are used in
an increasing number of machine learning problems, complex kernels have not,
yet, been used, in spite of their potential interest in applications that deal
with complex signals, with Communications being a typical example. In this
paper, we present a general framework to attack the problem of adaptive
filtering of complex signals, using either real reproducing kernels, taking
advantage of a technique called \textit{complexification} of real RKHSs, or
complex reproducing kernels, highlighting the use of the complex gaussian
kernel. In order to derive gradients of operators that need to be defined on
the associated complex RKHSs, we employ the powerful tool of Wirtinger's
Calculus, which has recently attracted attention in the signal processing
community. To this end, in this paper, the notion of Wirtinger's calculus is
extended, for the first time, to include complex RKHSs and use it to derive
several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm.
Experiments verify that the CKLMS offers significant performance improvements
over several linear and nonlinear algorithms, when dealing with nonlinearities.Comment: 15 pages (double column), preprint of article accepted in IEEE Trans.
Sig. Pro
Dominating sets and ego-centered decompositions in social networks
Our aim here is to address the problem of decomposing a whole network into a
minimal number of ego-centered subnetworks. For this purpose, the network egos
are picked out as the members of a minimum dominating set of the network.
However, to find such an efficient dominating ego-centered construction, we
need to be able to detect all the minimum dominating sets and to compare all
the corresponding dominating ego-centered decompositions of the network. To
find all the minimum dominating sets of the network, we are developing a
computational heuristic, which is based on the partition of the set of nodes of
a graph into three subsets, the always dominant vertices, the possible dominant
vertices and the never dominant vertices, when the domination number of the
network is known. To compare the ensuing dominating ego-centered decompositions
of the network, we are introducing a number of structural measures that count
the number of nodes and links inside and across the ego-centered subnetworks.
Furthermore, we are applying the techniques of graph domination and
ego=centered decomposition for six empirical social networks.Comment: 17 pages, 7 figure
Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems
We consider a class of linear ill-posed inverse problems arising from
inversion of a compact operator with singular values which decay exponentially
to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown
function. If the observational noise is assumed to be Gaussian then this prior
is conjugate to the likelihood so that the posterior distribution is also
Gaussian. We study Bayesian posterior consistency in the small observational
noise limit. We assume that the forward operator and the prior and noise
covariance operators commute with one another. We show how, for given
smoothness assumptions on the truth, the scale parameter of the prior can be
adjusted to optimize the rate of posterior contraction to the truth, and we
explicitly compute the logarithmic rate.Comment: 25 pages, 2 figure
Adversarial Inpainting of Medical Image Modalities
Numerous factors could lead to partial deteriorations of medical images. For
example, metallic implants will lead to localized perturbations in MRI scans.
This will affect further post-processing tasks such as attenuation correction
in PET/MRI or radiation therapy planning. In this work, we propose the
inpainting of medical images via Generative Adversarial Networks (GANs). The
proposed framework incorporates two patch-based discriminator networks with
additional style and perceptual losses for the inpainting of missing
information in realistically detailed and contextually consistent manner. The
proposed framework outperformed other natural image inpainting techniques both
qualitatively and quantitatively on two different medical modalities.Comment: To be submitted to ICASSP 201
Preamble-Based Channel Estimation for CP-OFDM and OFDM/OQAM Systems: A Comparative Study
In this paper, preamble-based least squares (LS) channel estimation in OFDM
systems of the QAM and offset QAM (OQAM) types is considered, in both the
frequency and the time domains. The construction of optimal (in the mean
squared error (MSE) sense) preambles is investigated, for both the cases of
full (all tones carrying pilot symbols) and sparse (a subset of pilot tones,
surrounded by nulls or data) preambles. The two OFDM systems are compared for
the same transmit power, which, for cyclic prefix (CP) based OFDM/QAM, also
includes the power spent for CP transmission. OFDM/OQAM, with a sparse preamble
consisting of equipowered and equispaced pilots embedded in zeros, turns out to
perform at least as well as CP-OFDM. Simulations results are presented that
verify the analysis
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