4,412 research outputs found
A Novel Convex Relaxation for Non-Binary Discrete Tomography
We present a novel convex relaxation and a corresponding inference algorithm
for the non-binary discrete tomography problem, that is, reconstructing
discrete-valued images from few linear measurements. In contrast to state of
the art approaches that split the problem into a continuous reconstruction
problem for the linear measurement constraints and a discrete labeling problem
to enforce discrete-valued reconstructions, we propose a joint formulation that
addresses both problems simultaneously, resulting in a tighter convex
relaxation. For this purpose a constrained graphical model is set up and
evaluated using a novel relaxation optimized by dual decomposition. We evaluate
our approach experimentally and show superior solutions both mathematically
(tighter relaxation) and experimentally in comparison to previously proposed
relaxations
Geometric reconstruction methods for electron tomography
Electron tomography is becoming an increasingly important tool in materials
science for studying the three-dimensional morphologies and chemical
compositions of nanostructures. The image quality obtained by many current
algorithms is seriously affected by the problems of missing wedge artefacts and
nonlinear projection intensities due to diffraction effects. The former refers
to the fact that data cannot be acquired over the full tilt range;
the latter implies that for some orientations, crystalline structures can show
strong contrast changes. To overcome these problems we introduce and discuss
several algorithms from the mathematical fields of geometric and discrete
tomography. The algorithms incorporate geometric prior knowledge (mainly
convexity and homogeneity), which also in principle considerably reduces the
number of tilt angles required. Results are discussed for the reconstruction of
an InAs nanowire
Non-convex image reconstruction via Expectation Propagation
Tomographic image reconstruction can be mapped to a problem of finding
solutions to a large system of linear equations which maximize a function that
includes \textit{a priori} knowledge regarding features of typical images such
as smoothness or sharpness. This maximization can be performed with standard
local optimization tools when the function is concave, but it is generally
intractable for realistic priors, which are non-concave. We introduce a new
method to reconstruct images obtained from Radon projections by using
Expectation Propagation, which allows us to reframe the problem from an
Bayesian inference perspective. We show, by means of extensive simulations,
that, compared to state-of-the-art algorithms for this task, Expectation
Propagation paired with very simple but non log-concave priors, is often able
to reconstruct images up to a smaller error while using a lower amount of
information per pixel. We provide estimates for the critical rate of
information per pixel above which recovery is error-free by means of
simulations on ensembles of phantom and real images.Comment: 12 pages, 6 figure
3D particle tracking velocimetry using dynamic discrete tomography
Particle tracking velocimetry in 3D is becoming an increasingly important
imaging tool in the study of fluid dynamics, combustion as well as plasmas. We
introduce a dynamic discrete tomography algorithm for reconstructing particle
trajectories from projections. The algorithm is efficient for data from two
projection directions and exact in the sense that it finds a solution
consistent with the experimental data. Non-uniqueness of solutions can be
detected and solutions can be tracked individually
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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