2,667 research outputs found
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
Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm
In phase retrieval, the goal is to recover a complex signal from the
magnitude of its linear measurements. While many well-known algorithms
guarantee deterministic recovery of the unknown signal using i.i.d. random
measurement matrices, they suffer serious convergence issues some
ill-conditioned matrices. As an example, this happens in optical imagers using
binary intensity-only spatial light modulators to shape the input wavefront.
The problem of ill-conditioned measurement matrices has also been a topic of
interest for compressed sensing researchers during the past decade. In this
paper, using recent advances in generic compressed sensing, we propose a new
phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary
matrices using both sparse and dense input signals. This algorithm is also
robust to the strong noise levels found in some imaging applications
Projected Multi-Agent Consensus Equilibrium (PMACE) for Distributed Reconstruction with Application to Ptychography
Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging
problem as a balance among multiple update agents such as data-fitting terms
and denoisers. However, each such agent operates on a separate copy of the full
image, leading to redundant memory use and slow convergence when each agent
affects only a small subset of the full image. In this paper, we extend MACE to
Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent
updates only a projected component of the full image, thus greatly reducing
memory use for some applications.We describe PMACE in terms of an equilibrium
problem and an equivalent fixed point problem and show that in most cases the
PMACE equilibrium is not the solution of an optimization problem. To
demonstrate the value of PMACE, we apply it to the problem of ptychography, in
which a sample is reconstructed from the diffraction patterns resulting from
coherent X-ray illumination at multiple overlapping spots. In our PMACE
formulation, each spot corresponds to a separate data-fitting agent, with the
final solution found as an equilibrium among all the agents. Our results
demonstrate that the PMACE reconstruction algorithm generates more accurate
reconstructions at a lower computational cost than existing ptychography
algorithms when the spots are sparsely sampled
Refractive shape from light field distortion
Acquiring transparent, refractive objects is challenging as these kinds of objects can only be observed by analyzing the distortion of reference background patterns. We present a new, single image approach to reconstructing thin transparent surfaces, such as thin solids or surfaces of fluids. Our method is based on observing the distortion of light field background illumination. Light field probes have the potential to encode up to four dimensions in varying colors and intensities: spatial and angular variation on the probe surface; commonly employed reference patterns are only two-dimensional by coding either position or angle on the probe. We show that the additional information can be used to reconstruct refractive surface normals and a sparse set of control points from a single photograph
Phase Retrieval for Partially Coherent Observations
Phase retrieval is in general a non-convex and non-linear task and the
corresponding algorithms struggle with the issue of local minima. We consider
the case where the measurement samples within typically very small and
disconnected subsets are coherently linked to each other - which is a
reasonable assumption for our objective of antenna measurements. Two classes of
measurement setups are discussed which can provide this kind of extra
information: multi-probe systems and holographic measurements with multiple
reference signals. We propose several formulations of the corresponding phase
retrieval problem. The simplest of these formulations poses a linear system of
equations similar to an eigenvalue problem where a unique non-trivial
null-space vector needs to be found. Accurate phase reconstruction for
partially coherent observations is, thus, possible by a reliable solution
process and with judgment of the solution quality. Under ideal, noise-free
conditions, the required sampling density is less than two times the number of
unknowns. Noise and other observation errors increase this value slightly.
Simulations for Gaussian random matrices and for antenna measurement scenarios
demonstrate that reliable phase reconstruction is possible with the presented
approach.Comment: 12 pages, 14 figure
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