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In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…
Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…
Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in…
We introduce the multivariate Log S-fBM model (mLog S-fBM), extending the univariate framework proposed by Wu \textit{et al.} to the multidimensional setting. We define the multidimensional Stationary fractional Brownian motion (mS-fBM),…
In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…
We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…
The present article is devoted to developing the Legendre wavelet operational matrix method (LWOMM) to find the numerical solution of two-dimensional hyperbolic telegraph equations (HTE) with appropriate initial time boundary space…
Long-term time series forecasting (LTSF) is a critical task in computational intelligence. While Transformer-based models effectively capture long-range dependencies, they often suffer from quadratic complexity and overfitting due to data…
This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation…
This work investigates spatial-mode multiplexing (SMM) for practical free-space optical communication (FSO) systems using direct detection. Unlike several works in the literature where mutually incoherent channels are assumed, we consider…
Light sheet fluorescence microscopy (LSM) enables high-resolution, three-dimensional (3D) imaging of biological specimens, providing rich volumetric data for studying cellular organization, pathology, and vascular networks. However, the…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We develop a wavelet like representation of functions in $L^p(\mathbb{R})$ based on their Fourier--Hermite coefficients; i.e., we describe an expansion of such functions where the local behavior of the terms characterize completely the…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
We find that the EPE evaluation metrics of RAFT-stereo converge inconsistently in the low and high frequency regions, resulting high frequency degradation (e.g., edges and thin objects) during the iterative process. The underlying reason…
This study formally adapts the time-domain linear sampling method (TLSM) for ultrasonic imaging of stationary and evolving fractures in safety-critical components. The TLSM indicator is then applied to the laboratory test data of [22, 18]…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The concept of $p$-adic quincunx Haar MRA was introduced and studied in~\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a $p$-adic MRA. We give an explicit description for all wavelet…