354 research outputs found
Deconvolution of confocal microscopy images using proximal iteration and sparse representations
We propose a deconvolution algorithm for images blurred and degraded by a
Poisson noise. The algorithm uses a fast proximal backward-forward splitting
iteration. This iteration minimizes an energy which combines a
\textit{non-linear} data fidelity term, adapted to Poisson noise, and a
non-smooth sparsity-promoting regularization (e.g -norm) over the image
representation coefficients in some dictionary of transforms (e.g. wavelets,
curvelets). Our results on simulated microscopy images of neurons and cells are
confronted to some state-of-the-art algorithms. They show that our approach is
very competitive, and as expected, the importance of the non-linearity due to
Poisson noise is more salient at low and medium intensities. Finally an
experiment on real fluorescent confocal microscopy data is reported
Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images
In this article, two closed and convex sets for blind deconvolution problem
are proposed. Most blurring functions in microscopy are symmetric with respect
to the origin. Therefore, they do not modify the phase of the Fourier transform
(FT) of the original image. As a result blurred image and the original image
have the same FT phase. Therefore, the set of images with a prescribed FT phase
can be used as a constraint set in blind deconvolution problems. Another convex
set that can be used during the image reconstruction process is the epigraph
set of Total Variation (TV) function. This set does not need a prescribed upper
bound on the total variation of the image. The upper bound is automatically
adjusted according to the current image of the restoration process. Both of
these two closed and convex sets can be used as a part of any blind
deconvolution algorithm. Simulation examples are presented.Comment: Submitted to IEEE Selected Topics in Signal Processin
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
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