6,283 research outputs found
Bayesian computation in imaging inverse problems with partially unknown models
Many imaging problems require solving a high-dimensional inverse problem that is
ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting
the value of the so-called regularisation parameters that control the amount of regularisation enforced. These parameters are notoriously difficult to set a priori and
can have a dramatic impact on the recovered estimates. In this thesis, we propose
a general empirical Bayesian method for setting regularisation parameters in imaging problems that are convex w.r.t. the unknown image. Our method calibrates
regularisation parameters directly from the observed data by maximum marginal
likelihood estimation, and can simultaneously estimate multiple regularisation parameters. A main novelty is that this maximum marginal likelihood estimation
problem is efficiently solved by using a stochastic proximal gradient algorithm that
is driven by two proximal Markov chain Monte Carlo samplers, thus intimately combining modern high-dimensional optimisation and stochastic sampling techniques.
Furthermore, the proposed algorithm uses the same basic operators as proximal optimisation algorithms, namely gradient and proximal operators, and it is therefore
straightforward to apply to problems that are currently solved by using proximal optimisation techniques. We also present a detailed theoretical analysis of the proposed
methodology, and demonstrate it with a range of experiments and comparisons with
alternative approaches from the literature. The considered experiments include image denoising, non-blind image deconvolution, and hyperspectral unmixing, using
synthesis and analysis priors involving the `1, total-variation, total-variation and
`1, and total-generalised-variation pseudo-norms. Moreover, we explore some other
applications of the proposed method including maximum marginal likelihood estimation in Bayesian logistic regression and audio compressed sensing, as well as an
application to model selection based on residuals
A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection
We propose a new space-variant anisotropic regularisation term for
variational image restoration, based on the statistical assumption that the
gradients of the target image distribute locally according to a bivariate
generalised Gaussian distribution. The highly flexible variational structure of
the corresponding regulariser encodes several free parameters which hold the
potential for faithfully modelling the local geometry in the image and
describing local orientation preferences. For an automatic estimation of such
parameters, we design a robust maximum likelihood approach and report results
on its reliability on synthetic data and natural images. For the numerical
solution of the corresponding image restoration model, we use an iterative
algorithm based on the Alternating Direction Method of Multipliers (ADMM). A
suitable preliminary variable splitting together with a novel result in
multivariate non-convex proximal calculus yield a very efficient minimisation
algorithm. Several numerical results showing significant quality-improvement of
the proposed model with respect to some related state-of-the-art competitors
are reported, in particular in terms of texture and detail preservation
Post processing of differential images for direct extrasolar planet detection from the ground
The direct imaging from the ground of extrasolar planets has become today a
major astronomical and biological focus. This kind of imaging requires
simultaneously the use of a dedicated high performance Adaptive Optics [AO]
system and a differential imaging camera in order to cancel out the flux coming
from the star. In addition, the use of sophisticated post-processing techniques
is mandatory to achieve the ultimate detection performance required. In the
framework of the SPHERE project, we present here the development of a new
technique, based on Maximum A Posteriori [MAP] approach, able to estimate
parameters of a faint companion in the vicinity of a bright star, using the
multi-wavelength images, the AO closed-loop data as well as some knowledge on
non-common path and differential aberrations. Simulation results show a 10^-5
detectivity at 5sigma for angular separation around 15lambda/D with only two
images.Comment: 12 pages, 6 figures, This paper will be published in the proceedings
of the conference Advances in Adaptive Optics (SPIE 6272), part of SPIE's
Astronomical Telescopes & Instrumentation, 24-31 May 2006, Orlando, F
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
Maximum Entropy Estimation of the Galactic Bulge Morphology via the VVV Red Clump
The abundance and narrow magnitude dispersion of Red Clump (RC) stars make
them a popular candidate for mapping the morphology of the bulge region of the
Milky Way. Using an estimate of the RC's intrinsic luminosity function, we
extracted the three-dimensional density distribution of the RC from deep
photometric catalogues of the VISTA Variables in the Via Lactea (VVV) survey.
We used maximum entropy based deconvolution to extract the spatial distribution
of the bulge from Ks-band star counts. We obtained our extrapolated
non-parametric model of the bulge over the inner 40 by 40 degrees squared
region of the Galactic centre. Our reconstruction also naturally matches onto a
parametric fit to the bulge outside the VVV region and inpaints overcrowded and
high extinction regions. We found a range of bulge properties consistent with
other recent investigations based on the VVV data. In particular, we estimated
the bulge mass to be in the range 13 to 17 billion solar masses, the
X-component to be between 18% and 25% of the bulge mass, and the bulge angle
with respect to the Sun-Galactic centre line to be between 18 and 32 degrees.
Studies of the Fermi Large Area Telescope (LAT) gamma-ray Galactic centre
excess suggests that the excess may be traced by Galactic bulge distributed
sources. We applied our deconvolved density in a template fitting analysis of
this Fermi-LAT GeV excess and found an improvement in the fit compared to
previous parametric based templates.Comment: 25 pages, 27 figures, minor typo correcte
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