11,239 research outputs found
Domain decomposition methods for compressed sensing
We present several domain decomposition algorithms for sequential and
parallel minimization of functionals formed by a discrepancy term with respect
to data and total variation constraints. The convergence properties of the
algorithms are analyzed. We provide several numerical experiments, showing the
successful application of the algorithms for the restoration 1D and 2D signals
in interpolation/inpainting problems respectively, and in a compressed sensing
problem, for recovering piecewise constant medical-type images from partial
Fourier ensembles.Comment: 4 page
Multi-frequency image reconstruction for radio-interferometry with self-tuned regularization parameters
As the world's largest radio telescope, the Square Kilometer Array (SKA) will
provide radio interferometric data with unprecedented detail. Image
reconstruction algorithms for radio interferometry are challenged to scale well
with TeraByte image sizes never seen before. In this work, we investigate one
such 3D image reconstruction algorithm known as MUFFIN (MUlti-Frequency image
reconstruction For radio INterferometry). In particular, we focus on the
challenging task of automatically finding the optimal regularization parameter
values. In practice, finding the regularization parameters using classical grid
search is computationally intensive and nontrivial due to the lack of ground-
truth. We adopt a greedy strategy where, at each iteration, the optimal
parameters are found by minimizing the predicted Stein unbiased risk estimate
(PSURE). The proposed self-tuned version of MUFFIN involves parallel and
computationally efficient steps, and scales well with large- scale data.
Finally, numerical results on a 3D image are presented to showcase the
performance of the proposed approach
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
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