4,598 research outputs found
An invitation to quantum tomography (II)
The quantum state of a light beam can be represented as an infinite
dimensional density matrix or equivalently as a density on the plane called the
Wigner function. We describe quantum tomography as an inverse statistical
problem in which the state is the unknown parameter and the data is given by
results of measurements performed on identical quantum systems. We present
consistency results for Pattern Function Projection Estimators as well as for
Sieve Maximum Likelihood Estimators for both the density matrix of the quantum
state and its Wigner function. Finally we illustrate via simulated data the
performance of the estimators. An EM algorithm is proposed for practical
implementation. There remain many open problems, e.g. rates of convergence,
adaptation, studying other estimators, etc., and a main purpose of the paper is
to bring these to the attention of the statistical community.Comment: An earlier version of this paper with more mathematical background
but less applied statistical content can be found on arXiv as
quant-ph/0303020. An electronic version of the paper with high resolution
figures (postscript instead of bitmaps) is available from the authors. v2:
added cross-validation results, reference
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
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