Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Technical Report: Improved Fourier Reconstruction using Jump Information
  with Applications to MRI   Certain applications such as Magnetic Resonance Imaging (MRI) require the
reconstruction of functions from Fourier spectral data. When the underlying
functions are piecewise-smooth, standard Fourier approximation methods suffer
from the Gibbs phenomenon - with associated oscillatory artifacts in the
vicinity of edges and an overall reduced order of convergence in the
approximation. This paper proposes an edge-augmented Fourier reconstruction
procedure which uses only the first few Fourier coefficients of an underlying
piecewise-smooth function to accurately estimate jump information and then
incorporate it into a Fourier partial sum approximation. We provide both
theoretical and empirical results showing the improved accuracy of the proposed
method, as well as comparisons demonstrating superior performance over existing
state-of-the-art sparse optimization-based methods. Extensions of the proposed
techniques to functions of several variables are also addressed preliminarily.
All code used to generate the results in this report are made publicly
available.

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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat