63 research outputs found
Sparse online variational Bayesian regression
This work considers variational Bayesian inference as an inexpensive and
scalable alternative to a fully Bayesian approach in the context of
sparsity-promoting priors. In particular, the priors considered arise from
scale mixtures of Normal distributions with a generalized inverse Gaussian
mixing distribution. This includes the variational Bayesian LASSO as an
inexpensive and scalable alternative to the Bayesian LASSO introduced in [65].
It also includes a family of priors which more strongly promote sparsity. For
linear models the method requires only the iterative solution of deterministic
least squares problems. Furthermore, for p unknown covariates the method can be
implemented exactly online with a cost of in computation and
in memory per iteration -- in other words, the cost per iteration is
independent of n, and in principle infinite data can be considered. For large
an approximation is able to achieve promising results for a cost of
per iteration, in both computation and memory. Strategies for hyper-parameter
tuning are also considered. The method is implemented for real and simulated
data. It is shown that the performance in terms of variable selection and
uncertainty quantification of the variational Bayesian LASSO can be comparable
to the Bayesian LASSO for problems which are tractable with that method, and
for a fraction of the cost. The present method comfortably handles ,
on a laptop in less than 30 minutes, and , overnight
Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging
In der angewandten Statistik können Regressionsmodelle mit hochdimensionalen Koeffizienten auftreten, die sich nicht mit gewöhnlichen Computersystemen schätzen lassen. Dies betrifft unter anderem die Analyse digitaler Bilder unter Berücksichtigung räumlich-zeitlicher Abhängigkeiten, wie sie innerhalb der medizinisch-biologischen Forschung häufig vorkommen.
In der vorliegenden Arbeit wird ein Verfahren formuliert, das in der
Lage ist, Regressionsmodelle mit hochdimensionalen Koeffizienten und nicht-normalverteilten Zielgrößen unter moderaten Anforderungen an die benötigte Hardware zu schätzen. Hierzu wird zunächst im Rahmen strukturiert additiver Regressionsmodelle aufgezeigt, worin die Limitationen aktueller Inferenzansätze bei der Anwendung auf hochdimensionale Problemstellungen liegen, sowie Möglichkeiten diskutiert, diese zu umgehen. Darauf basierend wird ein Algorithmus formuliert, dessen Stärken und Schwächen anhand von Simulationsstudien analysiert werden. Darüber hinaus findet das Verfahren Anwendung in drei verschiedenen Bereichen der medizinisch-biologischen Bildgebung und zeigt dadurch, dass es ein vielversprechender Kandidat für die Beantwortung hochdimensionaler Fragestellungen ist.In applied statistics regression models with high-dimensional
coefficients can occur which cannot be estimated using ordinary computers. Amongst others, this applies to the analysis of digital images taking spatio-temporal dependencies into account as they commonly occur within bio-medical research.
In this thesis a procedure is formulated which allows to fit regression
models with high-dimensional coefficients and non-normal response
values requiring only moderate computational equipment. To this end, limitations of different inference strategies for structured additive regression models are demonstrated when applied to high-dimensional problems and possible solutions are discussed. Based thereon an algorithm is formulated whose strengths and weaknesses are subsequently analyzed using simulation studies. Furthermore, the procedure is applied to three different fields of bio-medical imaging from which can be concluded that the algorithm is a promising candidate for answering high-dimensional problems
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Underwater image restoration: super-resolution and deblurring via sparse representation and denoising by means of marine snow removal
Underwater imaging has been widely used as a tool in many fields, however, a major issue is the quality of the resulting images/videos. Due to the light's interaction with water and its constituents, the acquired underwater images/videos often suffer from a significant amount of scatter (blur, haze) and noise. In the light of these issues, this thesis considers problems of low-resolution, blurred and noisy underwater images and proposes several approaches to improve the quality of such images/video frames.
Quantitative and qualitative experiments validate the success of proposed algorithms
Image Restoration
This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with
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