4,981 research outputs found
Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors
In this paper, we propose a Bayesian MAP estimator for solving the
deconvolution problems when the observations are corrupted by Poisson noise.
Towards this goal, a proper data fidelity term (log-likelihood) is introduced
to reflect the Poisson statistics of the noise. On the other hand, as a prior,
the images to restore are assumed to be positive and sparsely represented in a
dictionary of waveforms such as wavelets or curvelets. Both analysis and
synthesis-type sparsity priors are considered. Piecing together the data
fidelity and the prior terms, the deconvolution problem boils down to the
minimization of non-smooth convex functionals (for each prior). We establish
the well-posedness of each optimization problem, characterize the corresponding
minimizers, and solve them by means of proximal splitting algorithms
originating from the realm of non-smooth convex optimization theory.
Experimental results are conducted to demonstrate the potential applicability
of the proposed algorithms to astronomical imaging datasets
An Iterative Shrinkage Approach to Total-Variation Image Restoration
The problem of restoration of digital images from their degraded measurements
plays a central role in a multitude of practically important applications. A
particularly challenging instance of this problem occurs in the case when the
degradation phenomenon is modeled by an ill-conditioned operator. In such a
case, the presence of noise makes it impossible to recover a valuable
approximation of the image of interest without using some a priori information
about its properties. Such a priori information is essential for image
restoration, rendering it stable and robust to noise. Particularly, if the
original image is known to be a piecewise smooth function, one of the standard
priors used in this case is defined by the Rudin-Osher-Fatemi model, which
results in total variation (TV) based image restoration. The current arsenal of
algorithms for TV-based image restoration is vast. In the present paper, a
different approach to the solution of the problem is proposed based on the
method of iterative shrinkage (aka iterated thresholding). In the proposed
method, the TV-based image restoration is performed through a recursive
application of two simple procedures, viz. linear filtering and soft
thresholding. Therefore, the method can be identified as belonging to the group
of first-order algorithms which are efficient in dealing with images of
relatively large sizes. Another valuable feature of the proposed method
consists in its working directly with the TV functional, rather then with its
smoothed versions. Moreover, the method provides a single solution for both
isotropic and anisotropic definitions of the TV functional, thereby
establishing a useful connection between the two formulae.Comment: The paper was submitted to the IEEE Transactions on Image Processing
on October 22nd, 200
Map-making in small field modulated CMB polarisation experiments: approximating the maximum-likelihood method
Map-making presents a significant computational challenge to the next
generation of kilopixel CMB polarisation experiments. Years worth of time
ordered data (TOD) from thousands of detectors will need to be compressed into
maps of the T, Q and U Stokes parameters. Fundamental to the science goal of
these experiments, the observation of B-modes, is the ability to control noise
and systematics. In this paper, we consider an alternative to the
maximum-likelihood method, called destriping, where the noise is modelled as a
set of discrete offset functions and then subtracted from the time-stream. We
compare our destriping code (Descart: the DEStriping CARTographer) to a full
maximum-likelihood map-maker, applying them to 200 Monte-Carlo simulations of
time-ordered data from a ground based, partial-sky polarisation modulation
experiment. In these simulations, the noise is dominated by either detector or
atmospheric 1/f noise. Using prior information of the power spectrum of this
noise, we produce destriped maps of T, Q and U which are negligibly different
from optimal. The method does not filter the signal or bias the E or B-mode
power spectra. Depending on the length of the destriping baseline, the method
delivers between 5 and 22 times improvement in computation time over the
maximum-likelihood algorithm. We find that, for the specific case of single
detector maps, it is essential to destripe the atmospheric 1/f in order to
detect B-modes, even though the Q and U signals are modulated by a half-wave
plate spinning at 5-Hz.Comment: 18 pages, 17 figures, MNRAS accepted v2: content added (inc: table
2), typos correcte
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