17,751 research outputs found
Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals
We consider the problem of "algebraic reconstruction" of linear combinations
of shifts of several known signals from the Fourier samples.
Following \cite{Bat.Sar.Yom2}, for each we choose sampling set
to be a subset of the common set of zeroes of the Fourier transforms
, on which . It was shown
in \cite{Bat.Sar.Yom2} that in this way the reconstruction system is
"decoupled" into separate systems, each including only one of the signals
. The resulting systems are of a "generalized Prony" form.
However, the sampling sets as above may be non-uniform/not "dense enough" to
allow for a unique reconstruction of the shifts and amplitudes. In the present
paper we study uniqueness and robustness of non-uniform Fourier sampling of
signals as above, investigating sampling of exponential polynomials with purely
imaginary exponents. As the main tool we apply a well-known result in Harmonic
Analysis: the Tur\'an-Nazarov inequality (\cite{Naz}), and its generalization
to discrete sets, obtained in \cite{Fri.Yom}. We illustrate our general
approach with examples, and provide some simulation results
On the Design and Analysis of Multiple View Descriptors
We propose an extension of popular descriptors based on gradient orientation
histograms (HOG, computed in a single image) to multiple views. It hinges on
interpreting HOG as a conditional density in the space of sampled images, where
the effects of nuisance factors such as viewpoint and illumination are
marginalized. However, such marginalization is performed with respect to a very
coarse approximation of the underlying distribution. Our extension leverages on
the fact that multiple views of the same scene allow separating intrinsic from
nuisance variability, and thus afford better marginalization of the latter. The
result is a descriptor that has the same complexity of single-view HOG, and can
be compared in the same manner, but exploits multiple views to better trade off
insensitivity to nuisance variability with specificity to intrinsic
variability. We also introduce a novel multi-view wide-baseline matching
dataset, consisting of a mixture of real and synthetic objects with ground
truthed camera motion and dense three-dimensional geometry
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
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