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Shift-invariant spaces (SISs) on the real line provide a natural framework for representing, analyzing and processing signals with inherent shift-invariant structure. In this paper, we extend this framework to the finite undirected graph…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast ones in the frequency domain. Such an invertible…
High-resolution time-frequency (TF) analysis plays crucial role in characterizing multicomponent signal (MCSs) and estimating oscillatory properties. Linear time-frequency representations (TFRs) such as classical short-time Fourier…
This note develops the first-ever noise-centric anomaly prediction method for a fused discrete-time signal. A Wavelet Packet Transform (WPT) provides a time--frequency expansion in which structure and residual can be separated via…
This paper presents an adaptive waveform design method using Multi-Tone Sinusoidal Frequency Modulation (MTSFM). The MTSFM waveform's modulation function is represented as a finite Fourier series expansion. The Fourier coefficients are…
In photoacoustic tomography (PAT) with flat sensor, we routinely encounter two types of limited data. The first is due to using a finite sensor and is especially perceptible if the region of interest is large relative to the sensor or…
Neural networks for visual content understanding have recently evolved from convolutional ones (CNNs) to transformers. The prior (CNN) relies on small-windowed kernels to capture the regional clues, demonstrating solid local expressiveness.…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) are powerful techniques for the development of quantum procedures. They allow to derive circuits preparing desired polynomial transformations. Recent research…
The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black…
A generalized Nonlinear Fourier Transform (GNFT), which includes eigenvalues of higher multiplicity, is considered for information transmission over fiber optic channels. Numerical algorithms are developed to compute the direct and inverse…
In order to fully utilize spatial information for segmentation and address the challenge of handling areas with significant grayscale variations in remote sensing segmentation, we propose the SFFNet (Spatial and Frequency Domain Fusion…
State-of-the-art adaptive optics (AO) systems perform non-linear Fourier-type wavefront sensing for real-time corrections of dynamic wavefront aberrations. This general class of sensors uses a filtering mask in the focal plane that converts…
High spatial frequency information, including fine details like textures, significantly contributes to the accuracy of semantic segmentation. However, according to the Nyquist-Shannon Sampling Theorem, high-frequency components are…
The Continuous Wavelet Transform (CWT) is an effective tool for feature extraction in acoustic recognition using Convolutional Neural Networks (CNNs), particularly when applied to non-stationary audio. However, its high computational cost…
The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet…
Pansharpening aims to fuse high-resolution panchromatic (PAN) images with low-resolution multispectral (LRMS) images to generate high-resolution multispectral (HRMS) images. Although deep learning-based methods have achieved promising…
We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some $N$-length input vector in the presence of noise, where the $N$-point Walsh spectrum is $K$-sparse with $K = {O}(N^{\delta})$ scaling sub-linearly in the input…
Super-resolution (SR) aims to enhance the quality of low-resolution images and has been widely applied in medical imaging. We found that the design principles of most existing methods are influenced by SR tasks based on real-world images…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…