相关论文: Filtering with Wavelet Zeros and Gaussian Analytic…

The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…

This paper presents a rigorous theoretical convergence analysis of the Wirtinger Flow (WF) algorithm for Poisson phase retrieval, a fundamental problem in imaging applications. Unlike prior analyses that rely on truncation or additional…

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a…

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a…

We introduce $\texttt{WaveletNet}$, a wavelet-based neural network architecture to identify and reduce non-Gaussian noise in gravitational wave data. Traditionally, convolutional neural networks (CNNs) have been widely used as a flexible…

The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet…

Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…

A distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic…

The search for signatures of transient, unmodelled gravitational-wave (GW) bursts in the data of ground-based interferometric detectors typically uses `excess-power' search methods. One of the most challenging problems in the…

The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of Statistics…

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…

Classical Gaussian white noise in communications and signal processing is viewed as the limit of zero mean second order Gaussian processes with a compactly supported flat spectral density as the support goes to infinity. The difficulty of…

A wavelet-based changepoint method is proposed that determines when the variability of the noise in a sequence of functional profiles goes out-of-control from a known, fixed value. The functional portion of the profiles are allowed to come…

The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution…

The variational formulation of nonlinear filtering due to Mitter and Newton characterizes the filtering distribution as the unique minimizer of a free energy functional involving the relative entropy with respect to the prior and an…

This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density…

This paper studies recursive composite hypothesis testing in a network of sparsely connected agents. The network objective is to test a simple null hypothesis against a composite alternative concerning the state of the field, modeled as a…

Estimating the parameters of gravitational wave signals detected by ground-based detectors requires an understanding of the properties of the detectors' noise. In particular, the most commonly used likelihood function for gravitational wave…

We propose a wavelet-based technique for the nonparametric estimation of functions contaminated with noise whose mean and variance are linked via a possibly unknown variance function. Our method, termed the data-driven wavelet-Fisz…

Gravitational wave detectors now under construction are sensitive to the phase of the incident gravitational waves. Correspondingly, the signals from the different detectors can be combined, in the analysis, to simulate a single detector of…