相关论文: Convolution and Correlation Theorems for Wigner-Vi…

Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…

Convolutional neural networks have become a main tool for solving many machine vision and machine learning problems. A major element of these networks is the convolution operator which essentially computes the inner product between a weight…

Since their first applications, Convolutional Neural Networks (CNNs) have solved problems that have advanced the state-of-the-art in several domains. CNNs represent information using real numbers. Despite encouraging results, theoretical…

In computer vision, convolutional networks (CNNs) often adopts pooling to enlarge receptive field which has the advantage of low computational complexity. However, pooling can cause information loss and thus is detrimental to further…

We present a new Clifford-valued linear canonical Stockwell transform aimed at providing efficient and focused representation of Clifford-valued functions in high-dimensional time-frequency analysis. This transform improves upon the…

The use of quaternions as a novel tool for color image representation has yielded impressive results in color image processing. By considering the color image as a unified entity rather than separate color space components, quaternions can…

In this work, we describe examples for calculating the 1-D circular convolution of signals represented by 3-qubit superpositions. The case is considered, when the discrete Fourier transform of one of the signals is known and calculated in…

We study the covariance property of quadratic time-frequency distributions with respect to the action of the extended symplectic group. We show how covariance is related, and in fact in competition, with the possibility of damping the…

We consider a sequence of quantized Lorentzian pulses of non-interacting electrons impinging on a quantum point contact (QPC) and study the waiting time distribution (WTD), for any transmission and any number of pulses. As the degree of…

We recall the origin of angular ordering of soft parton emission in the region of small $x$ and show that this coherent structure can be detected in associated distributions. For structure functions at small $x$ and at fixed transverse…

We survey a new application of the Weil representation to construct a canonical basis of eigenvectors for the discrete Fourier transform (DFT). The transition matrix from the standard basis to the canonical basis defines a novel transform…

This paper introduces a novel time-frequency distribution, referred to as the Two-Dimensional Non-Separable Quadratic Phase Wigner Distribution (2D-NSQPWD), formulated within the framework of the Two-Dimensional Non-Separable Quadratic…

A Cumulant based method has been introduced to extract quantum corrections in distribution function with the equilibrium Wigner-Boltzmann equation. It is shown that unlike the moment expansion used in hydrodynamic model, cumulant expansion…

The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…

We propose a novel approach to image classification inspired by complex nonlinear biological visual processing, whereby classical convolutional neural networks (CNNs) are equipped with learnable higher-order convolutions. Our model…

The offset linear canonical transform (OLCT) provides a more general framework for a number of well known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical…

Multidimensional quaternion arrays (often referred to as "quaternion tensors") and their decompositions have recently gained increasing attention in various fields such as color and polarimetric imaging or video processing. Despite this…

Multi-color visible light communication (VLC) can increase throughput and enable joint lighting and communication operation, but practical color-based schemes such as color shift keying (CSK) typically rely on receiver optical filters whose…

A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…

The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…