29,218 research outputs found
Estimating hyperparameters and instrument parameters in regularized inversion. Illustration for SPIRE/Herschel map making
We describe regularized methods for image reconstruction and focus on the
question of hyperparameter and instrument parameter estimation, i.e.
unsupervised and myopic problems. We developed a Bayesian framework that is
based on the \post density for all unknown quantities, given the observations.
This density is explored by a Markov Chain Monte-Carlo sampling technique based
on a Gibbs loop and including a Metropolis-Hastings step. The numerical
evaluation relies on the SPIRE instrument of the Herschel observatory. Using
simulated and real observations, we show that the hyperparameters and
instrument parameters are correctly estimated, which opens up many perspectives
for imaging in astrophysics
Semi-blind Sparse Image Reconstruction with Application to MRFM
We propose a solution to the image deconvolution problem where the
convolution kernel or point spread function (PSF) is assumed to be only
partially known. Small perturbations generated from the model are exploited to
produce a few principal components explaining the PSF uncertainty in a high
dimensional space. Unlike recent developments on blind deconvolution of natural
images, we assume the image is sparse in the pixel basis, a natural sparsity
arising in magnetic resonance force microscopy (MRFM). Our approach adopts a
Bayesian Metropolis-within-Gibbs sampling framework. The performance of our
Bayesian semi-blind algorithm for sparse images is superior to previously
proposed semi-blind algorithms such as the alternating minimization (AM)
algorithm and blind algorithms developed for natural images. We illustrate our
myopic algorithm on real MRFM tobacco virus data.Comment: This work has been submitted to the IEEE Trans. Image Processing for
possible publicatio
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
Density mapping with weak lensing and phase information
The available probes of the large scale structure in the Universe have
distinct properties: galaxies are a high resolution but biased tracer of mass,
while weak lensing avoids such biases but, due to low signal-to-noise ratio,
has poor resolution. We investigate reconstructing the projected density field
using the complementarity of weak lensing and galaxy positions. We propose a
maximum-probability reconstruction of the 2D lensing convergence with a
likelihood term for shear data and a prior on the Fourier phases constructed
from the galaxy positions. By considering only the phases of the galaxy field,
we evade the unknown value of the bias and allow it to be calibrated by lensing
on a mode-by-mode basis. By applying this method to a realistic simulated
galaxy shear catalogue, we find that a weak prior on phases provides a good
quality reconstruction down to scales beyond l=1000, far into the noise domain
of the lensing signal alone.Comment: 11 pages, 9 figures, published in MNRA
Reducing "Structure From Motion": a General Framework for Dynamic Vision - Part 2: Experimental Evaluation
A number of methods have been proposed in the literature for estimating scene-structure and ego-motion from a sequence of images using dynamical models. Although all methods may be derived from a "natural" dynamical model within a unified framework, from an engineering perspective there are a number of trade-offs that lead to different strategies depending upon the specific applications and the goals one is targeting.
Which one is the winning strategy? In this paper we analyze the properties of the dynamical models that originate from each strategy under a variety of experimental conditions. For each model we assess the accuracy of the estimates, their robustness to measurement noise, sensitivity to initial conditions and visual angle, effects of the bas-relief ambiguity and occlusions, dependence upon the number of image measurements and their sampling rate
Identifiability of generalised Randles circuit models
The Randles circuit (including a parallel resistor and capacitor in series
with another resistor) and its generalised topology have widely been employed
in electrochemical energy storage systems such as batteries, fuel cells and
supercapacitors, also in biomedical engineering, for example, to model the
electrode-tissue interface in electroencephalography and baroreceptor dynamics.
This paper studies identifiability of generalised Randles circuit models, that
is, whether the model parameters can be estimated uniquely from the
input-output data. It is shown that generalised Randles circuit models are
structurally locally identifiable. The condition that makes the model structure
globally identifiable is then discussed. Finally, the estimation accuracy is
evaluated through extensive simulations
Reducing “Structure from Motion”: a general framework for dynamic vision. 2. Implementation and experimental assessment
For pt.1 see ibid., p.933-42 (1998). A number of methods have been proposed in the literature for estimating scene-structure and ego-motion from a sequence of images using dynamical models. Despite the fact that all methods may be derived from a “natural” dynamical model within a unified framework, from an engineering perspective there are a number of trade-offs that lead to different strategies depending upon the applications and the goals one is targeting. We want to characterize and compare the properties of each model such that the engineer may choose the one best suited to the specific application. We analyze the properties of filters derived from each dynamical model under a variety of experimental conditions, assess the accuracy of the estimates, their robustness to measurement noise, sensitivity to initial conditions and visual angle, effects of the bas-relief ambiguity and occlusions, dependence upon the number of image measurements and their sampling rate
On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models
This study investigates the effects of Markov chain Monte Carlo (MCMC)
sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is
restricted to the family of unnormalized probability densities for which the
negative log density (or energy function) is a ConvNet. We find that many of
the techniques used to stabilize training in previous studies are not
necessary. ML learning with a ConvNet potential requires only a few
hyper-parameters and no regularization. Using this minimal framework, we
identify a variety of ML learning outcomes that depend solely on the
implementation of MCMC sampling.
On one hand, we show that it is easy to train an energy-based model which can
sample realistic images with short-run Langevin. ML can be effective and stable
even when MCMC samples have much higher energy than true steady-state samples
throughout training. Based on this insight, we introduce an ML method with
purely noise-initialized MCMC, high-quality short-run synthesis, and the same
budget as ML with informative MCMC initialization such as CD or PCD. Unlike
previous models, our energy model can obtain realistic high-diversity samples
from a noise signal after training.
On the other hand, ConvNet potentials learned with non-convergent MCMC do not
have a valid steady-state and cannot be considered approximate unnormalized
densities of the training data because long-run MCMC samples differ greatly
from observed images. We show that it is much harder to train a ConvNet
potential to learn a steady-state over realistic images. To our knowledge,
long-run MCMC samples of all previous models lose the realism of short-run
samples. With correct tuning of Langevin noise, we train the first ConvNet
potentials for which long-run and steady-state MCMC samples are realistic
images.Comment: Code available at: https://github.com/point0bar1/ebm-anatom
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