Related papers: Wavelet invariants for statistically robust multi-…
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 propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and…
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
In this paper we present a wavelet based algorithm that is able to detect superimposed periodic signals in data with low signal-noise ratio. In this context, the results given by classical period determination methods highly depend on the…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
We develop a new approach to robust adaptive beamforming in the presence of signal steering vector errors. Since the signal steering vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the…
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to…
Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…
Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of…
Leveraging the symmetries inherent to specific data domains for the construction of equivariant neural networks has lead to remarkable improvements in terms of data efficiency and generalization. However, most existing research focuses on…
We present applications of variational -- wavelet approach to nonlinear (rational) rms envelope dynamics. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis.
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
Unsupervised deep learning has recently demonstrated the promise of producing high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data…
We report the first application of complex symmetric wavelets to the numerical simulation of a nonlinear signal propagation model. This model is the so-called nonlinear Schrodinger equation that describes, for instance, the evolution of the…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…