14,548 research outputs found
ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets
Wavelets and their associated transforms are highly efficient when
approximating and analyzing one-dimensional signals. However, multivariate
signals such as images or videos typically exhibit curvilinear singularities,
which wavelets are provably deficient of sparsely approximating and also of
analyzing in the sense of, for instance, detecting their direction. Shearlets
are a directional representation system extending the wavelet framework, which
overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful
implementation and fast associated transforms. In this paper, we will introduce
a comprehensive carefully documented software package coined ShearLab 3D
(www.ShearLab.org) and discuss its algorithmic details. This package provides
MATLAB code for a novel faithful algorithmic realization of the 2D and 3D
shearlet transform (and their inverses) associated with compactly supported
universal shearlet systems incorporating the option of using CUDA. We will
present extensive numerical experiments in 2D and 3D concerning denoising,
inpainting, and feature extraction, comparing the performance of ShearLab 3D
with similar transform-based algorithms such as curvelets, contourlets, or
surfacelets. In the spirit of reproducible reseaerch, all scripts are
accessible on www.ShearLab.org.Comment: There is another shearlet software package
(http://www.mathematik.uni-kl.de/imagepro/members/haeuser/ffst/) by S.
H\"auser and G. Steidl. We will include this in a revisio
Image interpolation using Shearlet based iterative refinement
This paper proposes an image interpolation algorithm exploiting sparse
representation for natural images. It involves three main steps: (a) obtaining
an initial estimate of the high resolution image using linear methods like FIR
filtering, (b) promoting sparsity in a selected dictionary through iterative
thresholding, and (c) extracting high frequency information from the
approximation to refine the initial estimate. For the sparse modeling, a
shearlet dictionary is chosen to yield a multiscale directional representation.
The proposed algorithm is compared to several state-of-the-art methods to
assess its objective as well as subjective performance. Compared to the cubic
spline interpolation method, an average PSNR gain of around 0.8 dB is observed
over a dataset of 200 images
Learning Points and Routes to Recommend Trajectories
The problem of recommending tours to travellers is an important and broadly
studied area. Suggested solutions include various approaches of
points-of-interest (POI) recommendation and route planning. We consider the
task of recommending a sequence of POIs, that simultaneously uses information
about POIs and routes. Our approach unifies the treatment of various sources of
information by representing them as features in machine learning algorithms,
enabling us to learn from past behaviour. Information about POIs are used to
learn a POI ranking model that accounts for the start and end points of tours.
Data about previous trajectories are used for learning transition patterns
between POIs that enable us to recommend probable routes. In addition, a
probabilistic model is proposed to combine the results of POI ranking and the
POI to POI transitions. We propose a new F score on pairs of POIs that
capture the order of visits. Empirical results show that our approach improves
on recent methods, and demonstrate that combining points and routes enables
better trajectory recommendations
Optimally sparse approximations of 3D functions by compactly supported shearlet frames
We study efficient and reliable methods of capturing and sparsely
representing anisotropic structures in 3D data. As a model class for
multidimensional data with anisotropic features, we introduce generalized
three-dimensional cartoon-like images. This function class will have two
smoothness parameters: one parameter \beta controlling classical smoothness and
one parameter \alpha controlling anisotropic smoothness. The class then
consists of piecewise C^\beta-smooth functions with discontinuities on a
piecewise C^\alpha-smooth surface. We introduce a pyramid-adapted, hybrid
shearlet system for the three-dimensional setting and construct frames for
L^2(R^3) with this particular shearlet structure. For the smoothness range
1<\alpha =< \beta =< 2 we show that pyramid-adapted shearlet systems provide a
nearly optimally sparse approximation rate within the generalized cartoon-like
image model class measured by means of non-linear N-term approximations.Comment: 56 pages, 6 figure
Globular clusters versus dark matter haloes in strong lensing observations
Small distortions in the images of Einstein rings or giant arcs offer the exciting prospect of detecting low mass dark matter haloes or subhaloes of mass below 109 M⊙ (for independent haloes, the mass refers to M200, and for subhaloes, the mass refers to the mass within tidal radius), most of which are too small to have made a visible galaxy. A very large number of such haloes are predicted to exist in the cold dark matter model of cosmogony; in contrast, other models, such as warm dark matter, predict no haloes below a mass of this order, which depends on the properties of the warm dark matter particle. Attempting to detect these small perturbers could therefore discriminate between different kinds of dark matter particles, and even rule out the cold dark matter model altogether. Globular clusters in the lens galaxy also induce distortions in the image, which could, in principle, contaminate the test. Here, we investigate the population of globular clusters in six early-type galaxies in the Virgo cluster. We find that the number density of globular clusters of mass MGC ∼ 106 M⊙ is comparable to that of the dark matter perturbers (subhaloes in the lenses and haloes along the line of sight of comparable mass). We show that the very different degrees of mass concentration in globular clusters and dark matter haloes result in different lensing distortions. These are detectable with milli-arcsecond resolution imaging, which can distinguish between globular cluster and dark matter halo signals
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