41,939 research outputs found
Cygnus A super-resolved via convex optimisation from VLA data
We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for
interferometric imaging, that is based on convex optimisation, for the
super-resolution of Cyg A from observations at the frequencies 8.422GHz and
6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average
sparsity and positivity priors enable image reconstruction beyond instrumental
resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is
developed for imaging in the presence of unknown noise levels and calibration
errors. We demonstrate the superior performance of the algorithm with respect
to the conventional CLEAN-based methods, reflected in super-resolved images
with high fidelity. The high resolution features of the recovered images are
validated by referring to maps of Cyg A at higher frequencies, more precisely
17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio
transient in Cyg A, revealed in the recovered images of the investigated data
sets. Our matlab code is available online on GitHub.Comment: 14 pages, 7 figures (3/7 animated figures), accepted for publication
in MNRA
Robust Multi-Image HDR Reconstruction for the Modulo Camera
Photographing scenes with high dynamic range (HDR) poses great challenges to
consumer cameras with their limited sensor bit depth. To address this, Zhao et
al. recently proposed a novel sensor concept - the modulo camera - which
captures the least significant bits of the recorded scene instead of going into
saturation. Similar to conventional pipelines, HDR images can be reconstructed
from multiple exposures, but significantly fewer images are needed than with a
typical saturating sensor. While the concept is appealing, we show that the
original reconstruction approach assumes noise-free measurements and quickly
breaks down otherwise. To address this, we propose a novel reconstruction
algorithm that is robust to image noise and produces significantly fewer
artifacts. We theoretically analyze correctness as well as limitations, and
show that our approach significantly outperforms the baseline on real data.Comment: to appear at the 39th German Conference on Pattern Recognition (GCPR)
201
Laplace deconvolution with noisy observations
In the present paper we consider Laplace deconvolution for discrete noisy
data observed on the interval whose length may increase with a sample size.
Although this problem arises in a variety of applications, to the best of our
knowledge, it has been given very little attention by the statistical
community. Our objective is to fill this gap and provide statistical treatment
of Laplace deconvolution problem with noisy discrete data. The main
contribution of the paper is explicit construction of an asymptotically
rate-optimal (in the minimax sense) Laplace deconvolution estimator which is
adaptive to the regularity of the unknown function. We show that the original
Laplace deconvolution problem can be reduced to nonparametric estimation of a
regression function and its derivatives on the interval of growing length T_n.
Whereas the forms of the estimators remain standard, the choices of the
parameters and the minimax convergence rates, which are expressed in terms of
T_n^2/n in this case, are affected by the asymptotic growth of the length of
the interval.
We derive an adaptive kernel estimator of the function of interest, and
establish its asymptotic minimaxity over a range of Sobolev classes. We
illustrate the theory by examples of construction of explicit expressions of
Laplace deconvolution estimators. A simulation study shows that, in addition to
providing asymptotic optimality as the number of observations turns to
infinity, the proposed estimator demonstrates good performance in finite sample
examples
Extended object reconstruction in adaptive-optics imaging: the multiresolution approach
We propose the application of multiresolution transforms, such as wavelets
(WT) and curvelets (CT), to the reconstruction of images of extended objects
that have been acquired with adaptive optics (AO) systems. Such multichannel
approaches normally make use of probabilistic tools in order to distinguish
significant structures from noise and reconstruction residuals. Furthermore, we
aim to check the historical assumption that image-reconstruction algorithms
using static PSFs are not suitable for AO imaging. We convolve an image of
Saturn taken with the Hubble Space Telescope (HST) with AO PSFs from the 5-m
Hale telescope at the Palomar Observatory and add both shot and readout noise.
Subsequently, we apply different approaches to the blurred and noisy data in
order to recover the original object. The approaches include multi-frame blind
deconvolution (with the algorithm IDAC), myopic deconvolution with
regularization (with MISTRAL) and wavelets- or curvelets-based static PSF
deconvolution (AWMLE and ACMLE algorithms). We used the mean squared error
(MSE) and the structural similarity index (SSIM) to compare the results. We
discuss the strengths and weaknesses of the two metrics. We found that CT
produces better results than WT, as measured in terms of MSE and SSIM.
Multichannel deconvolution with a static PSF produces results which are
generally better than the results obtained with the myopic/blind approaches
(for the images we tested) thus showing that the ability of a method to
suppress the noise and to track the underlying iterative process is just as
critical as the capability of the myopic/blind approaches to update the PSF.Comment: In revision in Astronomy & Astrophysics. 19 pages, 13 figure
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