17,526 research outputs found
Quality assessment by region in spot images fused by means dual-tree complex wavelet transform
This work is motivated in providing and evaluating a fusion algorithm of remotely sensed images, i.e. the fusion of a high spatial resolution panchromatic image with a multi-spectral image (also known as pansharpening) using the dual-tree complex wavelet transform (DT-CWT), an effective approach for conducting an analytic and oversampled wavelet transform to reduce aliasing, and in turn reduce shift dependence of the wavelet transform. The proposed scheme includes the definition of a model to establish how information will be extracted from the PAN band and how that information will be injected into the MS bands with low spatial resolution. The approach was applied to Spot 5 images where there are bands falling outside PANâs spectrum. We propose an optional step in the quality evaluation protocol, which is to study the quality of the merger by regions, where each region represents a specific feature of the image. The results show that DT-CWT based approach offers good spatial quality while retaining the spectral information of original images, case SPOT 5. The additional step facilitates the identification of the most affected regions by the fusion process
A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands
This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem
On The Continuous Steering of the Scale of Tight Wavelet Frames
In analogy with steerable wavelets, we present a general construction of
adaptable tight wavelet frames, with an emphasis on scaling operations. In
particular, the derived wavelets can be "dilated" by a procedure comparable to
the operation of steering steerable wavelets. The fundamental aspects of the
construction are the same: an admissible collection of Fourier multipliers is
used to extend a tight wavelet frame, and the "scale" of the wavelets is
adapted by scaling the multipliers. As an application, the proposed wavelets
can be used to improve the frequency localization. Importantly, the localized
frequency bands specified by this construction can be scaled efficiently using
matrix multiplication
Self-similar prior and wavelet bases for hidden incompressible turbulent motion
This work is concerned with the ill-posed inverse problem of estimating
turbulent flows from the observation of an image sequence. From a Bayesian
perspective, a divergence-free isotropic fractional Brownian motion (fBm) is
chosen as a prior model for instantaneous turbulent velocity fields. This
self-similar prior characterizes accurately second-order statistics of velocity
fields in incompressible isotropic turbulence. Nevertheless, the associated
maximum a posteriori involves a fractional Laplacian operator which is delicate
to implement in practice. To deal with this issue, we propose to decompose the
divergent-free fBm on well-chosen wavelet bases. As a first alternative, we
propose to design wavelets as whitening filters. We show that these filters are
fractional Laplacian wavelets composed with the Leray projector. As a second
alternative, we use a divergence-free wavelet basis, which takes implicitly
into account the incompressibility constraint arising from physics. Although
the latter decomposition involves correlated wavelet coefficients, we are able
to handle this dependence in practice. Based on these two wavelet
decompositions, we finally provide effective and efficient algorithms to
approach the maximum a posteriori. An intensive numerical evaluation proves the
relevance of the proposed wavelet-based self-similar priors.Comment: SIAM Journal on Imaging Sciences, 201
Cosmological constraints from the capture of non-Gaussianity in Weak Lensing data
Weak gravitational lensing has become a common tool to constrain the
cosmological model. The majority of the methods to derive constraints on
cosmological parameters use second-order statistics of the cosmic shear.
Despite their success, second-order statistics are not optimal and degeneracies
between some parameters remain. Tighter constraints can be obtained if
second-order statistics are combined with a statistic that is efficient to
capture non-Gaussianity. In this paper, we search for such a statistical tool
and we show that there is additional information to be extracted from
statistical analysis of the convergence maps beyond what can be obtained from
statistical analysis of the shear field. For this purpose, we have carried out
a large number of cosmological simulations along the {\sigma}8-{\Omega}m
degeneracy, and we have considered three different statistics commonly used for
non-Gaussian features characterization: skewness, kurtosis and peak count. To
be able to investigate non-Gaussianity directly in the shear field we have used
the aperture mass definition of these three statistics for different scales.
Then, the results have been compared with the results obtained with the same
statistics estimated in the convergence maps at the same scales. First, we show
that shear statistics give similar constraints to those given by convergence
statistics, if the same scale is considered. In addition, we find that the peak
count statistic is the best to capture non-Gaussianities in the weak lensing
field and to break the {\sigma}8-{\Omega}m degeneracy. We show that this
statistical analysis should be conducted in the convergence maps: first,
because there exist fast algorithms to compute the convergence map for
different scales, and secondly because it offers the opportunity to denoise the
reconstructed convergence map, which improves non-Gaussian features extraction.Comment: Accepted for publication in MNRAS (11 pages, 5 figures, 9 tables
The Haar Wavelet Transform of a Dendrogram: Additional Notes
We consider the wavelet transform of a finite, rooted, node-ranked, -way
tree, focusing on the case of binary () trees. We study a Haar wavelet
transform on this tree. Wavelet transforms allow for multiresolution analysis
through translation and dilation of a wavelet function. We explore how this
works in our tree context.Comment: 37 pp, 1 fig. Supplementary material to "The Haar Wavelet Transform
of a Dendrogram", http://arxiv.org/abs/cs.IR/060810
- âŠ