119 research outputs found
Robust nonparametric detection of objects in noisy images
We propose a novel statistical hypothesis testing method for detection of
objects in noisy images. The method uses results from percolation theory and
random graph theory. We present an algorithm that allows to detect objects of
unknown shapes in the presence of nonparametric noise of unknown level and of
unknown distribution. No boundary shape constraints are imposed on the object,
only a weak bulk condition for the object's interior is required. The algorithm
has linear complexity and exponential accuracy and is appropriate for real-time
systems. In this paper, we develop further the mathematical formalism of our
method and explore important connections to the mathematical theory of
percolation and statistical physics. We prove results on consistency and
algorithmic complexity of our testing procedure. In addition, we address not
only an asymptotic behavior of the method, but also a finite sample performance
of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049.
Link to the abstract at EURANDOM repository:
http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at
EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd
Multiple testing, uncertainty and realistic pictures
We study statistical detection of grayscale objects in noisy images. The
object of interest is of unknown shape and has an unknown intensity, that can
be varying over the object and can be negative. No boundary shape constraints
are imposed on the object, only a weak bulk condition for the object's interior
is required. We propose an algorithm that can be used to detect grayscale
objects of unknown shapes in the presence of nonparametric noise of unknown
level. Our algorithm is based on a nonparametric multiple testing procedure. We
establish the limit of applicability of our method via an explicit,
closed-form, non-asymptotic and nonparametric consistency bound. This bound is
valid for a wide class of nonparametric noise distributions. We achieve this by
proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report
2011-004. Link to the abstract at EURANDOM Repository:
http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at
EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd
Neural-network quantum state tomography
We revisit the application of neural networks techniques to quantum state
tomography. We confirm that the positivity constraint can be successfully
implemented with trained networks that convert outputs from standard
feed-forward neural networks to valid descriptions of quantum states. Any
standard neural-network architecture can be adapted with our method. Our
results open possibilities to use state-of-the-art deep-learning methods for
quantum state reconstruction under various types of noise.Comment: 8 pages, 4 color figures. Comments are most welcom
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