Related papers: On optimal wavelet bases for the realization of mi…

We provide a detailed analysis of the obstruction (studied first by S. Durand and later by R. Yin and one of us) in the construction of multidirectional wavelet orthonormal bases corresponding to any admissible frequency partition in the…

The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings…

Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

In this paper, we describe some recent results obtained in the context of vector subdivision schemes which possess the so-called full rank property. Such kind of schemes, in particular those which have an interpolatory nature, are connected…

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…

The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…

In this paper, we design mother wavelets for the 1D continuous wavelet transform with some optimality properties. An optimal mother wavelet here is one that has an ambiguity function with minimal spread in the continuous coefficient space…

Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…

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…

This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…

To date, various speech technology systems have adopted the vocoder approach, a method for synthesizing speech waveform that shows a major role in the performance of statistical parametric speech synthesis. WaveNet one of the best models…

In the case of multi-parameter full-waveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradient-based minimization is used,…

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…

We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…

Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…

We introduce WaveSim, a multi-scale similarity metric for the evaluation of spatial fields in weather and climate applications. WaveSim exploits wavelet transforms to decompose input fields into scale-specific wavelet coefficients. The…

While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a…