Related papers: Atangana-Baleanu Regularized Wavelet Compression F…
This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared…
This paper describes the implementation of polycomp, a open-sourced, publicly available program for compressing one-dimensional data series in tabular format. The program is particularly suited for compressing smooth, noiseless streams of…
This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the…
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…
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…
We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the Discrete Wavelet Transform (DWT) to the input signal,…
Standard apodization methods suppress side lobes but increase FWHM, reducing lateral resolution. Grating lobes can interfere with the main lobe, introducing artifacts in ultrasound images. A simple mathematical apodization function is…
It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock.…
We consider a class of porous medium type of equations with Caputo time derivative. The prototype problem reads as $\Dc u=-\A u^m$ and is posed on a bounded Euclidean domain $\Omega\subset\mathbb{R}^N$ with zero Dirichlet boundary…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
This paper establishes new sufficient conditions for Mittag-Leffler stability of Caputo fractional-order nonlinear systems with state-dependent delays. The central analytical tool is a class of Lyapunov-Krasovskii functionals that…
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption…
We present a treatise on solving the Takagi-Taupin equations in the case of a strain field with an additional, spatially slowly varying component (owing to \emph{e.g.}~heat expansion or angular compression). We show that the presence of…
We demonstrate experimentally and numerically that the application of a partially coherent beam (PCB) in combination with time averaging leads to a significant reduction in the scintillation index. We use a simplified experimental approach…
Noise is a significant challenge in imaging. Conventional intensity-based techniques mitigate noise through various filtering methods, but they often require prior knowledge of noise characteristics and struggle, especially under low-light…
Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…
We aim to automatize the identification of collective variables to simplify and speed up enhanced sampling simulations of conformational dynamics in biomolecules. We focus on anharmonic low-frequency vibrations that exhibit fluctuations on…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…