Related papers: Intrinsic wavelet regression for curves of Hermiti…
This paper develops intrinsic wavelet denoising methods for surfaces of Hermitian positive definite matrices, with in mind the application to nonparametric estimation of the time-varying spectral matrix of a multivariate locally stationary…
In this paper we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. This estimator preserves positive-definiteness and enjoys…
Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian…
Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial…
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…
In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as Riemannian manifolds or Lie groups. We rely on the strong connection between wavelets and…
Successful wavelet estimation is an essential step for seismic methods like impedance inversion, analysis of amplitude variations with offset and full waveform inversion. Homomorphic deconvolution has long intrigued as a potentially elegant…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curves modulo shape-preserving transformations. We summarize the…
The Multiscale Fourier Transform of a seismic trace performs time-frequency analyses over a range of window lengths. The variation in window length captures local and global relative amplitudes between events, thereby allowing reflectivity…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
In this paper we are discussing various aspects of wavelet filters. While there are earlier studies of these filters as matrix valued functions in wavelets, in signal processing, and in systems, we here expand the framework. Motivated by…
Invariances in neural networks are useful and necessary for many tasks. However, the representation of the invariance of most neural network models has not been characterized. We propose measures to quantify the invariance of neural…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…