2,138 research outputs found
Extracting HI cosmological signal with Generalized Needlet Internal Linear Combination
HI intensity mapping is a new observational technique to map fluctuations in
the large-scale structure of matter using the 21 cm emission line of atomic
hydrogen (HI). Sensitive radio surveys have the potential to detect Baryon
Acoustic Oscillations (BAO) at low redshifts (z < 1) in order to constrain the
properties of dark energy. Observations of the HI signal will be contaminated
by instrumental noise and, more significantly, by astrophysical foregrounds,
such as Galactic synchrotron emission, which is at least four orders of
magnitude brighter than the HI signal. Foreground cleaning is recognised as one
of the key challenges for future radio astronomy surveys. We study the ability
of the Generalized Needlet Internal Linear Combination (GNILC) method to
subtract radio foregrounds and to recover the cosmological HI signal for a
general HI intensity mapping experiment. The GNILC method is a new technique
that uses both frequency and spatial information to separate the components of
the observed data. Our results show that the method is robust to the complexity
of the foregrounds. For simulated radio observations including HI emission,
Galactic synchrotron, Galactic free-free, radio sources and 0.05 mK thermal
noise, we find that we can reconstruct the HI power spectrum for multipoles 30
< l < 150 with 6% accuracy on 50% of the sky for a redshift z ~ 0.25.Comment: 20 pages, 13 figures. Updated to match version accepted by MNRA
Foreground component separation with generalised ILC
The 'Internal Linear Combination' (ILC) component separation method has been
extensively used to extract a single component, the CMB, from the WMAP
multifrequency data. We generalise the ILC approach for separating other
millimetre astrophysical emissions. We construct in particular a
multidimensional ILC filter, which can be used, for instance, to estimate the
diffuse emission of a complex component originating from multiple correlated
emissions, such as the total emission of the Galactic interstellar medium. The
performance of such generalised ILC methods, implemented on a needlet frame, is
tested on simulations of Planck mission observations, for which we successfully
reconstruct a low noise estimate of emission from astrophysical foregrounds
with vanishing CMB and SZ contamination.Comment: 11 pages, 6 figures (2 figures added), 1 reference added,
introduction expanded, V2: version accepted by MNRA
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
Data-driven time-frequency analysis of multivariate data
Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition
and time-frequency analysis of real world nonstationary signals. Its main advantages over
other time-frequency methods are its locality, data-driven nature, multiresolution-based
decomposition, higher time-frequency resolution and its ability to capture oscillation of
any type (nonharmonic signals). These properties have made EMD a viable tool for real
world nonstationary data analysis.
Recent advances in sensor and data acquisition technologies have brought to light
new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore,
imperative to design multivariate extensions of the existing nonlinear and nonstationary
analysis algorithms as they are expected to give more insight into the dynamics and the
interdependence between multiple channels of such signals.
To this end, this thesis presents multivariate extensions of the empirical mode de-
composition algorithm and illustrates their advantages with regards to multivariate non-
stationary data analysis. Some important properties of such extensions are also explored,
including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple
data channels. Owing to the generality of the proposed methods, an improved multi-
variate EMD-based algorithm is introduced which solves some inherent problems in the
original EMD algorithm. Finally, to demonstrate the potential of the proposed methods,
simulations on the fusion of multiple real world signals (wind, images and inertial body
motion data) support the analysis
Wavelet/shearlet hybridized neural networks for biomedical image restoration
Recently, new programming paradigms have emerged that combine parallelism and numerical computations with algorithmic differentiation. This approach allows for the hybridization of neural network techniques for inverse imaging problems with more traditional methods such as wavelet-based sparsity modelling techniques. The benefits are twofold: on the one hand traditional methods with well-known properties can be integrated in neural networks, either as separate layers or tightly integrated in the network, on the other hand, parameters in traditional methods can be trained end-to-end from datasets in a neural network "fashion" (e.g., using Adagrad or Adam optimizers). In this paper, we explore these hybrid neural networks in the context of shearlet-based regularization for the purpose of biomedical image restoration. Due to the reduced number of parameters, this approach seems a promising strategy especially when dealing with small training data sets
The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch
Recent and forthcoming advances in instrumentation, and giant new surveys,
are creating astronomical data sets that are not amenable to the methods of
analysis familiar to astronomers. Traditional methods are often inadequate not
merely because of the size in bytes of the data sets, but also because of the
complexity of modern data sets. Mathematical limitations of familiar algorithms
and techniques in dealing with such data sets create a critical need for new
paradigms for the representation, analysis and scientific visualization (as
opposed to illustrative visualization) of heterogeneous, multiresolution data
across application domains. Some of the problems presented by the new data sets
have been addressed by other disciplines such as applied mathematics,
statistics and machine learning and have been utilized by other sciences such
as space-based geosciences. Unfortunately, valuable results pertaining to these
problems are mostly to be found only in publications outside of astronomy. Here
we offer brief overviews of a number of concepts, techniques and developments,
some "old" and some new. These are generally unknown to most of the
astronomical community, but are vital to the analysis and visualization of
complex datasets and images. In order for astronomers to take advantage of the
richness and complexity of the new era of data, and to be able to identify,
adopt, and apply new solutions, the astronomical community needs a certain
degree of awareness and understanding of the new concepts. One of the goals of
this paper is to help bridge the gap between applied mathematics, artificial
intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in
Astronomy, special issue "Robotic Astronomy
2D-1D Wavelet Reconstruction As A Tool For Source Finding In Spectroscopic Imaging Surveys
Today, image denoising by thresholding of wavelet coefficients is a commonly
used tool for 2D image enhancement. Since the data product of spectroscopic
imaging surveys has two spatial and one spectral dimension, the techniques for
denoising have to be adapted to this change in dimensionality. In this paper we
will review the basic method of denoising data by thresholding wavelet
coefficients and implement a 2D-1D wavelet decomposition to obtain an efficient
way of denoising spectroscopic data cubes. We conduct different simulations to
evaluate the usefulness of the algorithm as part of a source finding pipeline.Comment: 8 pages, 7 figures, 1 table, accepted for publication in PASA Special
Issue on Source Finding and Visualizatio
Bounded PCA based Multi Sensor Image Fusion Employing Curvelet Transform Coefficients
The fusion of thermal and visible images acts as an important device for target detection. The quality of the spectral content of the fused image improves with wavelet-based image fusion. However, compared to PCA-based fusion, most wavelet-based methods provide results with a lower spatial resolution. The outcome gets better when the two approaches are combined, but they may still be refined. Compared to wavelets, the curvelet transforms more accurately depict the edges in the image. Enhancing the edges is a smart way to improve spatial resolution and the edges are crucial for interpreting the images. The fusion technique that utilizes curvelets enables the provision of additional data in both spectral and spatial areas concurrently. In this paper, we employ an amalgamation of Curvelet Transform and a Bounded PCA (CTBPCA) method to fuse thermal and visible images. To evidence the enhanced efficiency of our proposed technique, multiple evaluation metrics and comparisons with existing image merging methods are employed. Our approach outperforms others in both qualitative and quantitative analysis, except for runtime performance. Future Enhancement-The study will be based on using the fused image for target recognition. Future work should also focus on this method’s continued improvement and optimization for real-time video processing
- …