Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction from projections using dynamics: Non-Stochastic Case   The problem of determining three-dimensional density fields from single
two-dimensional projections is hopelessly underdetermined without additional
assumptions. While parameterized inversions are typically used to solve this
problem, we present theoretical results along a different route to the
elimination of indeterminacy. Suppose that we have a series of N radiographs
measuring X-ray or proton attenuation through an evolving object at a sequence
of times. Suppose also that we know the deterministic dynamical laws governing
the evolution of the object we are probing with radiography. The these laws can
be used to combine the radiographs into one "super"-measurement which can then
be inverted to the object sequence. Now suppose the objects are points in $R^n$
and the radiographs are points in $R^d$. It would be expected that the best we
could do would be to get invertability when N = $\lceil n/d \rceil$. The worst
case is that we never get invertability. We look at both cases carefully for
linear dynamics. We show that dynamical laws giving this optimally short
invertibility time are generic. We then illustrate with numerical examples and
present a conjecture for the nonlinear case.

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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an