857 research outputs found
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
A Framework for Directional and Higher-Order Reconstruction in Photoacoustic Tomography
Photoacoustic tomography is a hybrid imaging technique that combines high
optical tissue contrast with high ultrasound resolution. Direct reconstruction
methods such as filtered backprojection, time reversal and least squares suffer
from curved line artefacts and blurring, especially in case of limited angles
or strong noise. In recent years, there has been great interest in regularised
iterative methods. These methods employ prior knowledge on the image to provide
higher quality reconstructions. However, easy comparisons between regularisers
and their properties are limited, since many tomography implementations heavily
rely on the specific regulariser chosen. To overcome this bottleneck, we
present a modular reconstruction framework for photoacoustic tomography. It
enables easy comparisons between regularisers with different properties, e.g.
nonlinear, higher-order or directional. We solve the underlying minimisation
problem with an efficient first-order primal-dual algorithm. Convergence rates
are optimised by choosing an operator dependent preconditioning strategy. Our
reconstruction methods are tested on challenging 2D synthetic and experimental
data sets. They outperform direct reconstruction approaches for strong noise
levels and limited angle measurements, offering immediate benefits in terms of
acquisition time and quality. This work provides a basic platform for the
investigation of future advanced regularisation methods in photoacoustic
tomography.Comment: submitted to "Physics in Medicine and Biology". Changes from v1 to
v2: regularisation with directional wavelet has been added; new experimental
tests have been include
Radio Astronomy Image Reconstruction in the Big Data Era
Next generation radio interferometric telescopes pave the way for the future of radio astronomy with extremely wide-fields of view and precision polarimetry not possible at other optical wavelengths, with the required cost of image reconstruction. These instruments will be used to map large scale Galactic and extra-galactic structures at higher resolution and fidelity than ever before. However, radio astronomy has entered the era of big data, limiting the expected sensitivity and fidelity of the instruments due to the large amounts of data. New image reconstruction methods are critical to meet the data requirements needed to obtain new scientific discoveries in radio astronomy. To meet this need, this work takes traditional radio astronomical imaging and introduces new of state-of-the-art image reconstruction frameworks of sparse image reconstruction algorithms. The software package PURIFY, developed in this work, uses convex optimization algorithms (i.e. alternating direction method of multipliers) to solve for the reconstructed image. We design, implement, and apply distributed radio interferometric image reconstruction methods for the message passing interface (MPI), showing that PURIFY scales to big data image reconstruction on computing clusters. We design a distributed wide-field imaging algorithm for non-coplanar arrays, while providing new theoretical insights for wide-field imaging. It is shown that PURIFY’s methods provide higher dynamic range than traditional image reconstruction methods, providing a more accurate and detailed sky model for real observations. This sets the stage for state-of-the-art image reconstruction methods to be distributed and applied to next generation interferometric telescopes, where they can be used to meet big data challenges and to make new scientific discoveries in radio astronomy and astrophysics
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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