60,408 research outputs found
A model-based iterative learning approach for diffuse optical tomography
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a ‘model-based’ learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration
Bayesian Strong Gravitational-Lens Modeling on Adaptive Grids: Objective Detection of Mass Substructure in Galaxies
We introduce a new adaptive and fully Bayesian grid-based method to model
strong gravitational lenses with extended images. The primary goal of this
method is to quantify the level of luminous and dark-mass substructure in
massive galaxies, through their effect on highly-magnified arcs and Einstein
rings. The method is adaptive on the source plane, where a Delaunay
tessellation is defined according to the lens mapping of a regular grid onto
the source plane. The Bayesian penalty function allows us to recover the best
non-linear potential-model parameters and/or a grid-based potential correction
and to objectively quantify the level of regularization for both the source and
the potential. In addition, we implement a Nested-Sampling technique to
quantify the errors on all non-linear mass model parameters -- ... -- and allow
an objective ranking of different potential models in terms of the marginalized
evidence. In particular, we are interested in comparing very smooth lens mass
models with ones that contain mass-substructures. The algorithm has been tested
on a range of simulated data sets, created from a model of a realistic lens
system. One of the lens systems is characterized by a smooth potential with a
power-law density profile, twelve include a NFW dark-matter substructure of
different masses and at different positions and one contains two NFW dark
substructures with the same mass but with different positions. Reconstruction
of the source and of the lens potential for all of these systems shows the
method is able, in a realistic scenario, to identify perturbations with masses
>=10^7 solar mass when located on the Einstein ring. For positions both inside
and outside of the ring, masses of at least 10^9 solar mass are required (...).Comment: 21 pages, 15 figures, 4 tables; accepted for publication in MNRA
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
Semiparametric Bayesian models for human brain mapping
Functional magnetic resonance imaging (fMRI) has led to enormous progress in human brain mapping. Adequate analysis of the massive spatiotemporal data sets generated by this imaging technique, combining parametric and non-parametric components, imposes challenging problems in statistical modelling. Complex hierarchical Bayesian models in combination with computer-intensive Markov chain Monte Carlo inference are promising tools.The purpose of this paper is twofold. First, it provides a review of general semiparametric Bayesian models for the analysis of fMRI data. Most approaches focus on important but separate temporal or spatial aspects of the overall problem, or they proceed by stepwise procedures. Therefore, as a second aim, we suggest a complete spatiotemporal model for analysing fMRI data within a unified semiparametric Bayesian framework. An application to data from a visual stimulation experiment illustrates our approach and demonstrates its computational feasibility
Shape Modeling with Spline Partitions
Shape modelling (with methods that output shapes) is a new and important task
in Bayesian nonparametrics and bioinformatics. In this work, we focus on
Bayesian nonparametric methods for capturing shapes by partitioning a space
using curves. In related work, the classical Mondrian process is used to
partition spaces recursively with axis-aligned cuts, and is widely applied in
multi-dimensional and relational data. The Mondrian process outputs
hyper-rectangles. Recently, the random tessellation process was introduced as a
generalization of the Mondrian process, partitioning a domain with non-axis
aligned cuts in an arbitrary dimensional space, and outputting polytopes.
Motivated by these processes, in this work, we propose a novel parallelized
Bayesian nonparametric approach to partition a domain with curves, enabling
complex data-shapes to be acquired. We apply our method to HIV-1-infected human
macrophage image dataset, and also simulated datasets sets to illustrate our
approach. We compare to support vector machines, random forests and
state-of-the-art computer vision methods such as simple linear iterative
clustering super pixel image segmentation. We develop an R package that is
available at
\url{https://github.com/ShufeiGe/Shape-Modeling-with-Spline-Partitions}
BRUNO: A Deep Recurrent Model for Exchangeable Data
We present a novel model architecture which leverages deep learning tools to
perform exact Bayesian inference on sets of high dimensional, complex
observations. Our model is provably exchangeable, meaning that the joint
distribution over observations is invariant under permutation: this property
lies at the heart of Bayesian inference. The model does not require variational
approximations to train, and new samples can be generated conditional on
previous samples, with cost linear in the size of the conditioning set. The
advantages of our architecture are demonstrated on learning tasks that require
generalisation from short observed sequences while modelling sequence
variability, such as conditional image generation, few-shot learning, and
anomaly detection.Comment: NIPS 201
Extended Object Tracking: Introduction, Overview and Applications
This article provides an elaborate overview of current research in extended
object tracking. We provide a clear definition of the extended object tracking
problem and discuss its delimitation to other types of object tracking. Next,
different aspects of extended object modelling are extensively discussed.
Subsequently, we give a tutorial introduction to two basic and well used
extended object tracking approaches - the random matrix approach and the Kalman
filter-based approach for star-convex shapes. The next part treats the tracking
of multiple extended objects and elaborates how the large number of feasible
association hypotheses can be tackled using both Random Finite Set (RFS) and
Non-RFS multi-object trackers. The article concludes with a summary of current
applications, where four example applications involving camera, X-band radar,
light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are
highlighted.Comment: 30 pages, 19 figure
Serial Correlations in Single-Subject fMRI with Sub-Second TR
When performing statistical analysis of single-subject fMRI data, serial
correlations need to be taken into account to allow for valid inference.
Otherwise, the variability in the parameter estimates might be under-estimated
resulting in increased false-positive rates. Serial correlations in fMRI data
are commonly characterized in terms of a first-order autoregressive (AR)
process and then removed via pre-whitening. The required noise model for the
pre-whitening depends on a number of parameters, particularly the repetition
time (TR). Here we investigate how the sub-second temporal resolution provided
by simultaneous multislice (SMS) imaging changes the noise structure in fMRI
time series. We fit a higher-order AR model and then estimate the optimal AR
model order for a sequence with a TR of less than 600 ms providing whole brain
coverage. We show that physiological noise modelling successfully reduces the
required AR model order, but remaining serial correlations necessitate an
advanced noise model. We conclude that commonly used noise models, such as the
AR(1) model, are inadequate for modelling serial correlations in fMRI using
sub-second TRs. Rather, physiological noise modelling in combination with
advanced pre-whitening schemes enable valid inference in single-subject
analysis using fast fMRI sequences
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A Spatio-Temporal Bayesian Network Classifier for Understanding Visual Field Deterioration
Progressive loss of the field of vision is characteristic of a number of eye diseases
such as glaucoma which is a leading cause of irreversible blindness in the world. Recently,
there has been an explosion in the amount of data being stored on patients who suffer from visual deterioration including field test data, retinal image data and patient demographic data. However, there has been relatively little work in modelling
the spatial and temporal relationships common to such data. In this paper we introduce a novel method for classifying Visual Field (VF) data that explicitly models these spatial and temporal relationships. We carry out an analysis of this
method and compare it to a number of classifiers from the machine learning and statistical communities. Results are very encouraging showing that our classifiers are comparable to existing statistical models whilst also facilitating the understanding of underlying spatial and temporal relationships within VF data. The results
reveal the potential of using such models for knowledge discovery within ophthalmic databases, such as networks reflecting the ‘nasal step’, an early indicator of the onset of glaucoma. The results outlined in this paper pave the way for a substantial program of study involving many other spatial and temporal datasets, including retinal image and clinical data
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