Related papers: Multiscale Optimal Filtering on the Sphere
The atmosphere is one of the most important contamination sources in the ground-based Cosmic Microwave Background (CMB) observations. In this paper, we study three kinds of filters, which are polynomial filter, high-pass filter, and Wiener…
Curvelets are efficient to represent highly anisotropic signal content, such as a local linear and curvilinear structure. First-generation curvelets on the sphere, however, suffered from blocking artefacts. We present a new…
Image processing researchers commonly assert that "median filtering is better than linear filtering for removing noise in the presence of edges." Using a straightforward large-$n$ decision-theory framework, this folk-theorem is seen to be…
The contribution of this study is twofold: First, we propose an efficient algorithm for the computation of the (weighted) maximum likelihood estimators for the parameters of the multivariate Student-$t$ distribution, which we call…
In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph…
A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these…
In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
The extraction of signals from noise is a common problem in all areas of science and engineering. A particularly useful version is that of forecasting: determining a causal filter that estimates a future value of a hidden process from past…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
The WMAP satellite has made available high quality maps of the sky in five frequency bands ranging from 22 to 94 GHz, with the main scientific objective of studying the anisotropies of the Cosmic Microwave Background (CMB). These maps,…
We describe new methods for denoising and detection of gravitational waves embedded in additive Gaussian noise. The methods are based on Total Variation denoising algorithms. These algorithms, which do not need any a priori information…
We present an alternative method to filter a distribution, that is strictly confined within a sphere of given radius $r_c$, so that its Fourier transform is optimally confined within another sphere of radius $k_c$. In electronic structure…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
In the near-field context, the Fresnel approximation is typically employed to mathematically represent solvable functions of spherical waves. However, these efforts may fail to take into account the significant increase in the lower limit…
In the absence of a pure noise-free image it is hard to define what noise is, in any original noisy image, and as a consequence also where it is, and in what amount. In fact, the definition of noise depends largely on our own aim in the…
In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
We present a robust and efficient numerical framework based on a median filter scheme for solving a broad class of interface-related optimization problems, from image segmentation to topology optimization. A key innovation of our work is…
We present a new method of wavelet packet decomposition to be used in gravitational wave detection. An issue in wavelet analysis is what is the time-frequency resolution which is best suited to analyze data when in quest of a signal of…