Related papers: Application of Wavelets to Filtering of Noisy Data
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
Datasets (semi-)automatically collected from the web can easily scale to millions of entries, but a dataset's usefulness is directly related to how clean and high-quality its examples are. In this paper, we describe and publicly release an…
In some previous papers we proposed the use of free software for a processing of the Google satellite imagery. Here we discuss the use of a wavelet filter for the same purposes. This filter is a tool included in a freely downloadable…
Weak gravitational lensing is a very sensitive way of measuring cosmological parameters, including dark energy, and of testing current theories of gravitation. In practice, this requires exquisite measurement of the shapes of billions of…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…
We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We combine two Gaussianization techniques - Wavelet Non-Linear Wiener Filter (WNLWF) and density reconstruction - to quantify the recovery of Fisher information that is lost in the gravitational collapse. We compute a displacement fields,…
Acquired images for medical and other purposes can be affected by noise from both the equipment used in the capturing or the environment. This can have adverse effect on the information therein. Thus, the need to restore the image to its…
For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common…
A typical approach to developing an analysis algorithm for analyzing gravitational wave data is to assume a particular waveform and use its characteristics to formulate a detection criteria. Once a detection has been made, the algorithm…
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets…
Noisy supervision refers to supervising image restoration learning with noisy targets. It can alleviate the data collection burden and enhance the practical applicability of deep learning techniques. However, existing methods suffer from…
Recent medical imaging studies have given rise to distinct but inter-related datasets corresponding to multiple experimental tasks or longitudinal visits. Standard scalar-on-image regression models that fit each dataset separately are not…
In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the…
As borders between different regions, lines are an important element of natural images. Already at the level of the mammalian primary visual cortex (V1), neurons respond best to lines of a given orientation. We reduce a set of images to…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
Central to the gravitational wave detection problem is the challenge of separating features in the data produced by astrophysical sources from features produced by the detector. Matched filtering provides an optimal solution for Gaussian…