263 research outputs found
Maximum likelihood extension for non-circulant deconvolution
The International Conference on Image Processing, Paris, France, October 27-30 2014Directly applying circular de-convolution to real-world blurred images usually results in boundary artifacts. Classic boundary extension techniques fail to provide likely results, in terms of a circular boundary-condition observation model. Boundary reflection gives raise to non-smooth features, especially when oblique oriented features encounter the image boundaries. Tapering the boundaries of the image support, or similar strategies (like constrained diffusion), provides smoothness on the toroidal support; however this does not guarantee consistency with the spectral properties of the blur (in particular, to its zeros). Here we propose a simple, yet effective, model-derived method for extending real-world blurred images, so that they become likely in terms of a Gaussian circular boundary-condition observation model. We achieve artifact-free results, even under highly unfavorable conditions, when other methods fail.Peer Reviewe
Making Maps Of The Cosmic Microwave Background: The MAXIMA Example
This work describes Cosmic Microwave Background (CMB) data analysis
algorithms and their implementations, developed to produce a pixelized map of
the sky and a corresponding pixel-pixel noise correlation matrix from time
ordered data for a CMB mapping experiment. We discuss in turn algorithms for
estimating noise properties from the time ordered data, techniques for
manipulating the time ordered data, and a number of variants of the maximum
likelihood map-making procedure. We pay particular attention to issues
pertinent to real CMB data, and present ways of incorporating them within the
framework of maximum likelihood map-making. Making a map of the sky is shown to
be not only an intermediate step rendering an image of the sky, but also an
important diagnostic stage, when tests for and/or removal of systematic effects
can efficiently be performed. The case under study is the MAXIMA data set.
However, the methods discussed are expected to be applicable to the analysis of
other current and forthcoming CMB experiments.Comment: Replaced to match the published version, only minor change
Restoration of Poissonian Images Using Alternating Direction Optimization
Much research has been devoted to the problem of restoring Poissonian images,
namely for medical and astronomical applications. However, the restoration of
these images using state-of-the-art regularizers (such as those based on
multiscale representations or total variation) is still an active research
area, since the associated optimization problems are quite challenging. In this
paper, we propose an approach to deconvolving Poissonian images, which is based
on an alternating direction optimization method. The standard regularization
(or maximum a posteriori) restoration criterion, which combines the Poisson
log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to
hard optimization problems: the log-likelihood is non-quadratic and
non-separable, the regularizer is non-smooth, and there is a non-negativity
constraint. Using standard convex analysis tools, we present sufficient
conditions for existence and uniqueness of solutions of these optimization
problems, for several types of regularizers: total-variation, frame-based
analysis, and frame-based synthesis. We attack these problems with an instance
of the alternating direction method of multipliers (ADMM), which belongs to the
family of augmented Lagrangian algorithms. We study sufficient conditions for
convergence and show that these are satisfied, either under total-variation or
frame-based (analysis and synthesis) regularization. The resulting algorithms
are shown to outperform alternative state-of-the-art methods, both in terms of
speed and restoration accuracy.Comment: 12 pages, 12 figures, 2 tables. Submitted to the IEEE Transactions on
Image Processin
Fundamental Imaging Limits of Radio Telescope Arrays
The fidelity of radio astronomical images is generally assessed by practical
experience, i.e. using rules of thumb, although some aspects and cases have
been treated rigorously. In this paper we present a mathematical framework
capable of describing the fundamental limits of radio astronomical imaging
problems. Although the data model assumes a single snapshot observation, i.e.
variations in time and frequency are not considered, this framework is
sufficiently general to allow extension to synthesis observations. Using tools
from statistical signal processing and linear algebra, we discuss the
tractability of the imaging and deconvolution problem, the redistribution of
noise in the map by the imaging and deconvolution process, the covariance of
the image values due to propagation of calibration errors and thermal noise and
the upper limit on the number of sources tractable by self calibration. The
combination of covariance of the image values and the number of tractable
sources determines the effective noise floor achievable in the imaging process.
The effective noise provides a better figure of merit than dynamic range since
it includes the spatial variations of the noise. Our results provide handles
for improving the imaging performance by design of the array.Comment: 12 pages, 8 figure
Structural Variability from Noisy Tomographic Projections
In cryo-electron microscopy, the 3D electric potentials of an ensemble of
molecules are projected along arbitrary viewing directions to yield noisy 2D
images. The volume maps representing these potentials typically exhibit a great
deal of structural variability, which is described by their 3D covariance
matrix. Typically, this covariance matrix is approximately low-rank and can be
used to cluster the volumes or estimate the intrinsic geometry of the
conformation space. We formulate the estimation of this covariance matrix as a
linear inverse problem, yielding a consistent least-squares estimator. For
images of size -by- pixels, we propose an algorithm for calculating this
covariance estimator with computational complexity
, where the condition number
is empirically in the range --. Its efficiency relies on the
observation that the normal equations are equivalent to a deconvolution problem
in 6D. This is then solved by the conjugate gradient method with an appropriate
circulant preconditioner. The result is the first computationally efficient
algorithm for consistent estimation of 3D covariance from noisy projections. It
also compares favorably in runtime with respect to previously proposed
non-consistent estimators. Motivated by the recent success of eigenvalue
shrinkage procedures for high-dimensional covariance matrices, we introduce a
shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We
evaluate our methods on simulated datasets and achieve classification results
comparable to state-of-the-art methods in shorter running time. We also present
results on clustering volumes in an experimental dataset, illustrating the
power of the proposed algorithm for practical determination of structural
variability.Comment: 52 pages, 11 figure
Semi-Blind Spatially-Variant Deconvolution in Optical Microscopy with Local Point Spread Function Estimation By Use Of Convolutional Neural Networks
We present a semi-blind, spatially-variant deconvolution technique aimed at
optical microscopy that combines a local estimation step of the point spread
function (PSF) and deconvolution using a spatially variant, regularized
Richardson-Lucy algorithm. To find the local PSF map in a computationally
tractable way, we train a convolutional neural network to perform regression of
an optical parametric model on synthetically blurred image patches. We
deconvolved both synthetic and experimentally-acquired data, and achieved an
improvement of image SNR of 1.00 dB on average, compared to other deconvolution
algorithms.Comment: 2018/02/11: submitted to IEEE ICIP 2018 - 2018/05/04: accepted to
IEEE ICIP 201
Non-parametric PSF estimation from celestial transit solar images using blind deconvolution
Context: Characterization of instrumental effects in astronomical imaging is
important in order to extract accurate physical information from the
observations. The measured image in a real optical instrument is usually
represented by the convolution of an ideal image with a Point Spread Function
(PSF). Additionally, the image acquisition process is also contaminated by
other sources of noise (read-out, photon-counting). The problem of estimating
both the PSF and a denoised image is called blind deconvolution and is
ill-posed.
Aims: We propose a blind deconvolution scheme that relies on image
regularization. Contrarily to most methods presented in the literature, our
method does not assume a parametric model of the PSF and can thus be applied to
any telescope.
Methods: Our scheme uses a wavelet analysis prior model on the image and weak
assumptions on the PSF. We use observations from a celestial transit, where the
occulting body can be assumed to be a black disk. These constraints allow us to
retain meaningful solutions for the filter and the image, eliminating trivial,
translated and interchanged solutions. Under an additive Gaussian noise
assumption, they also enforce noise canceling and avoid reconstruction
artifacts by promoting the whiteness of the residual between the blurred
observations and the cleaned data.
Results: Our method is applied to synthetic and experimental data. The PSF is
estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for
SDO/AIA using the 2012 Venus transit. Results show that the proposed
non-parametric blind deconvolution method is able to estimate the core of the
PSF with a similar quality to parametric methods proposed in the literature. We
also show that, if these parametric estimations are incorporated in the
acquisition model, the resulting PSF outperforms both the parametric and
non-parametric methods.Comment: 31 pages, 47 figure
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