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This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…

Deep learning techniques have revolutionized the infrared and visible image fusion (IVIF), showing remarkable efficacy on complex scenarios. However, current methods do not fully combine frequency domain features with global semantic…

Within the area of applied harmonic analysis, various multiscale systems such as wavelets, ridgelets, curvelets, and shearlets have been introduced and successfully applied. The key property of each of those systems are their (optimal)…

This work proposes a mixed learning-based and optimization-based approach to the weighted-sum-rates beamforming problem in a multiple-input multiple-output (MIMO) wireless network. The conventional methods, i.e., the fractional programming…

In the evolving wireless communications landscape, addressing the challenges of multipath fading and high mobility remains paramount. This paper introduces the Unified Sequency-Frequency Multiplexing (USFM) framework, a pioneering…

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…

Producing reliable acoustic subsurface velocity models still remains the main bottleneck of the oil and gas industry's traditional imaging sequence. In complex geological settings, the output of conventional ray-based or wave-equation-based…

Many examples of signals and images cannot be modeled by locally bounded functions, so that the standard multifractal analysis, based on the H\"older exponent, is not feasible. We present a multifractal analysis based on another quantity,…

Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of…

Deep learning-based fault diagnosis (FD) approaches require a large amount of training data, which are difficult to obtain since they are located across different entities. Federated learning (FL) enables multiple clients to collaboratively…

This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…

There is rising interest in using Machine Learning (ML) model predictions as outcomes in causal analysis. However, these methods have faced challenges in finding the true treatment effects. It is also challenging to make choices about which…

Phased array ultrasound is a widely used technique in non-destructive testing. Using piezoelectric elements as both sources and receivers provides a significant gain in information and enables more accurate defect detection. When all…

Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant…

Wavefront-marking X-ray imaging techniques use e.g., sandpaper or a grating to generate intensity fluctuations, and analyze their distortion by the sample in order to retrieve attenuation, phase-contrast, and dark-field information. Phase…

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…

Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…

Multi-center transition metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information processing devices and storage units. For any practical application of MCTMs as magnetic units, it is…

Fractional programming (FP) arises in various communications and signal processing problems because several key quantities in the field are fractionally structured, e.g., the Cram\'{e}r-Rao bound, the Fisher information, and the…

We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…