1,320 research outputs found
Primordial Power Spectrum Reconstruction
In order to reconstruct the initial conditions of the universe it is
important to devise a method that can efficiently constrain the shape of the
power spectrum of primordial matter density fluctuations in a model-independent
way from data. In an earlier paper we proposed a method based on the wavelet
expansion of the primordial power spectrum. The advantage of this method is
that the orthogonality and multiresolution properties of wavelet basis
functions enable information regarding the shape of to be
encoded in a small number of non-zero coefficients. Any deviation from
scale-invariance can then be easily picked out. Here we apply this method to
simulated data to demonstrate that it can accurately reconstruct an input
, and present a prescription for how this method should be used
on future data.Comment: 4 pages, 2 figures. JCAP accepted versio
Locally adaptive image denoising by a statistical multiresolution criterion
We demonstrate how one can choose the smoothing parameter in image denoising
by a statistical multiresolution criterion, both globally and locally. Using
inhomogeneous diffusion and total variation regularization as examples for
localized regularization schemes, we present an efficient method for locally
adaptive image denoising. As expected, the smoothing parameter serves as an
edge detector in this framework. Numerical examples illustrate the usefulness
of our approach. We also present an application in confocal microscopy
A Common-Factor Approach for Multivariate Data Cleaning with an Application to Mars Phoenix Mission Data
Data quality is fundamentally important to ensure the reliability of data for
stakeholders to make decisions. In real world applications, such as scientific
exploration of extreme environments, it is unrealistic to require raw data
collected to be perfect. As data miners, when it is infeasible to physically
know the why and the how in order to clean up the data, we propose to seek the
intrinsic structure of the signal to identify the common factors of
multivariate data. Using our new data driven learning method, the common-factor
data cleaning approach, we address an interdisciplinary challenge on
multivariate data cleaning when complex external impacts appear to interfere
with multiple data measurements. Existing data analyses typically process one
signal measurement at a time without considering the associations among all
signals. We analyze all signal measurements simultaneously to find the hidden
common factors that drive all measurements to vary together, but not as a
result of the true data measurements. We use common factors to reduce the
variations in the data without changing the base mean level of the data to
avoid altering the physical meaning.Comment: 12 pages, 10 figures, 1 tabl
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