270 research outputs found
A Convex Semi-Definite Positive Framework for DTI Estimation and Regularization
International audienceIn this paper we introduce a novel variational method for joint estimation and regularization of diffusion tensor fields from noisy raw data. To this end, we use the classic quadratic data fidelity term derived from the Stejskal-Tanner equation with a new smoothness term leading to a convex objective function. The regularization term is based on the assumption that the signal can be reconstructed using a weighted average of observations on a local neighborhood. The weights measure the similarity between tensors and are computed directly from the diffusion images. We preserve the positive semi-definiteness constraint using a projected gradient descent. Experimental validation and comparisons with a similar method using synthetic data with known noise model, as well as classification of tensors towards understanding the anatomy of human skeletal muscle demonstrate the potential of our method
Median and related local filters for tensor-valued images
We develop a concept for the median filtering of tensor data. The main part of this concept is the definition of median for symmetric matrices. This definition is based on the minimisation of a geometrically motivated objective function which measures the sum of distances of a variable matrix to the given data matrices. This theoretically wellfounded concept fits into a context of similarly defined median filters for other multivariate data. Unlike some other approaches, we do not require by definition that the median has to be one of the given data values. Nevertheless, it happens so in many cases, equipping the matrix-valued median even with root signals similar to the scalar-valued situation. Like their scalar-valued counterparts, matrix-valued median filters show excellent capabilities for structure-preserving denoising. Experiments on diffusion tensor imaging, fluid dynamics and orientation estimation data are shown to demonstrate this. The orientation estimation examples give rise to a new variant of a robust adaptive structure tensor which can be compared to existing concepts. For the efficient computation of matrix medians, we present a convex programming framework. By generalising the idea of the matrix median filters, we design a variety of other local matrix filters. These include matrix-valued mid-range filters and, more generally, M-smoothers but also weighted medians and \alpha-quantiles. Mid-range filters and quantiles allow also interesting cross-links to fundamental concepts of matrix morphology
Hypothesis Testing For Network Data in Functional Neuroimaging
In recent years, it has become common practice in neuroscience to use
networks to summarize relational information in a set of measurements,
typically assumed to be reflective of either functional or structural
relationships between regions of interest in the brain. One of the most basic
tasks of interest in the analysis of such data is the testing of hypotheses, in
answer to questions such as "Is there a difference between the networks of
these two groups of subjects?" In the classical setting, where the unit of
interest is a scalar or a vector, such questions are answered through the use
of familiar two-sample testing strategies. Networks, however, are not Euclidean
objects, and hence classical methods do not directly apply. We address this
challenge by drawing on concepts and techniques from geometry, and
high-dimensional statistical inference. Our work is based on a precise
geometric characterization of the space of graph Laplacian matrices and a
nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate
our resulting methodologies for testing in the context of networks derived from
functional neuroimaging data on human subjects from the 1000 Functional
Connectomes Project. In particular, we show that this global test is more
statistical powerful, than a mass-univariate approach. In addition, we have
also provided a method for visualizing the individual contribution of each edge
to the overall test statistic.Comment: 34 pages. 5 figure
Total variation regularization for manifold-valued data
We consider total variation minimization for manifold valued data. We propose
a cyclic proximal point algorithm and a parallel proximal point algorithm to
minimize TV functionals with -type data terms in the manifold case.
These algorithms are based on iterative geodesic averaging which makes them
easily applicable to a large class of data manifolds. As an application, we
consider denoising images which take their values in a manifold. We apply our
algorithms to diffusion tensor images, interferometric SAR images as well as
sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds
(which includes the data space in diffusion tensor imaging) we show the
convergence of the proposed TV minimizing algorithms to a global minimizer
Learning Sparse Adversarial Dictionaries For Multi-Class Audio Classification
Audio events are quite often overlapping in nature, and more prone to noise
than visual signals. There has been increasing evidence for the superior
performance of representations learned using sparse dictionaries for
applications like audio denoising and speech enhancement. This paper
concentrates on modifying the traditional reconstructive dictionary learning
algorithms, by incorporating a discriminative term into the objective function
in order to learn class-specific adversarial dictionaries that are good at
representing samples of their own class at the same time poor at representing
samples belonging to any other class. We quantitatively demonstrate the
effectiveness of our learned dictionaries as a stand-alone solution for both
binary as well as multi-class audio classification problems.Comment: Accepted in Asian Conference of Pattern Recognition (ACPR-2017
Total Generalized Variation for Manifold-valued Data
In this paper we introduce the notion of second-order total generalized
variation (TGV) regularization for manifold-valued data in a discrete setting.
We provide an axiomatic approach to formalize reasonable generalizations of TGV
to the manifold setting and present two possible concrete instances that
fulfill the proposed axioms. We provide well-posedness results and present
algorithms for a numerical realization of these generalizations to the manifold
setup. Further, we provide experimental results for synthetic and real data to
further underpin the proposed generalization numerically and show its potential
for applications with manifold-valued data
A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit
In this paper, we consider the contextual variant of the MNL-Bandit problem.
More specifically, we consider a dynamic set optimization problem, where a
decision-maker offers a subset (assortment) of products to a consumer and
observes their response in every round. Consumers purchase products to maximize
their utility. We assume that a set of attributes describes the products, and
the mean utility of a product is linear in the values of these attributes. We
model consumer choice behavior using the widely used Multinomial Logit (MNL)
model and consider the decision maker problem of dynamically learning the model
parameters while optimizing cumulative revenue over the selling horizon .
Though this problem has attracted considerable attention in recent times, many
existing methods often involve solving an intractable non-convex optimization
problem. Their theoretical performance guarantees depend on a problem-dependent
parameter which could be prohibitively large. In particular, existing
algorithms for this problem have regret bounded by ,
where is a problem-dependent constant that can have an exponential
dependency on the number of attributes. In this paper, we propose an optimistic
algorithm and show that the regret is bounded by ,
significantly improving the performance over existing methods. Further, we
propose a convex relaxation of the optimization step, which allows for
tractable decision-making while retaining the favourable regret guarantee.Comment: updated version, under revie
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