9,135 research outputs found
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
Paving the way for transitions --- a case for Weyl geometry
This paper presents three aspects by which the Weyl geometric generalization
of Riemannian geometry, and of Einstein gravity, sheds light on actual
questions of physics and its philosophical reflection. After introducing the
theory's principles, it explains how Weyl geometric gravity relates to
Jordan-Brans-Dicke theory. We then discuss the link between gravity and the
electroweak sector of elementary particle physics, as it looks from the Weyl
geometric perspective. Weyl's hypothesis of a preferred scale gauge, setting
Weyl scalar curvature to a constant, gets new support from the interplay of the
gravitational scalar field and the electroweak one (the Higgs field). This has
surprising consequences for cosmological models. In particular it leads to a
static (Weyl geometric) spacetime with "inbuilt" cosmological redshift. This
may be used for putting central features of the present cosmological model into
a wider perspective.Comment: 54 pp, 2 figs. To appear in D. Lehmkuhl (ed.) "Towards a Theory of
Spacetime Theories", Einstein Studies, Basel: Birkhaeuser), revised version
June 201
Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates
The study of cerebral anatomy in developing neonates is of great importance for
the understanding of brain development during the early period of life. This
dissertation therefore focuses on three challenges in the modelling of cerebral
anatomy in neonates during brain development. The methods that have been
developed all use Magnetic Resonance Images (MRI) as source data.
To facilitate study of vascular development in the neonatal period, a set of image
analysis algorithms are developed to automatically extract and model cerebral
vessel trees. The whole process consists of cerebral vessel tracking from
automatically placed seed points, vessel tree generation, and vasculature
registration and matching. These algorithms have been tested on clinical Time-of-
Flight (TOF) MR angiographic datasets.
To facilitate study of the neonatal cortex a complete cerebral cortex segmentation
and reconstruction pipeline has been developed. Segmentation of the neonatal
cortex is not effectively done by existing algorithms designed for the adult brain
because the contrast between grey and white matter is reversed. This causes pixels
containing tissue mixtures to be incorrectly labelled by conventional methods. The
neonatal cortical segmentation method that has been developed is based on a novel
expectation-maximization (EM) method with explicit correction for mislabelled
partial volume voxels. Based on the resulting cortical segmentation, an implicit
surface evolution technique is adopted for the reconstruction of the cortex in
neonates. The performance of the method is investigated by performing a detailed
landmark study.
To facilitate study of cortical development, a cortical surface registration algorithm
for aligning the cortical surface is developed. The method first inflates extracted
cortical surfaces and then performs a non-rigid surface registration using free-form
deformations (FFDs) to remove residual alignment. Validation experiments using
data labelled by an expert observer demonstrate that the method can capture local
changes and follow the growth of specific sulcus
On the use of SIFT features for face authentication
Several pattern recognition and classification techniques
have been applied to the biometrics domain. Among them,
an interesting technique is the Scale Invariant Feature
Transform (SIFT), originally devised for object recognition.
Even if SIFT features have emerged as a very powerful image
descriptors, their employment in face analysis context
has never been systematically investigated.
This paper investigates the application of the SIFT approach
in the context of face authentication. In order to determine
the real potential and applicability of the method,
different matching schemes are proposed and tested using
the BANCA database and protocol, showing promising results
Fast reconstruction of 3D blood flows from Doppler ultrasound images and reduced models
This paper deals with the problem of building fast and reliable 3D
reconstruction methods for blood flows for which partial information is given
by Doppler ultrasound measurements. This task is of interest in medicine since
it could enrich the available information used in the diagnosis of certain
diseases which is currently based essentially on the measurements coming from
ultrasound devices. The fast reconstruction of the full flow can be performed
with state estimation methods that have been introduced in recent years and
that involve reduced order models. One simple and efficient strategy is the
so-called Parametrized Background Data-Weak approach (PBDW). It is a linear
mapping that consists in a least squares fit between the measurement data and a
linear reduced model to which a certain correction term is added. However, in
the original approach, the reduced model is built a priori and independently of
the reconstruction task (typically with a proper orthogonal decomposition or a
greedy algorithm). In this paper, we investigate the construction of other
reduced spaces which are built to be better adapted to the reconstruction task
and which result in mappings that are sometimes nonlinear. We compare the
performance of the different algorithms on numerical experiments involving
synthetic Doppler measurements. The results illustrate the superiority of the
proposed alternatives to the classical linear PBDW approach
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