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

In signal processing and identification, generalized singular value decomposition (GSVD), related to a sequence of matrices in product/quotient form are essential numerical linear algebra tools. On behalf of the growing demand for efficient…

The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…

The majority of medical images, especially those that resemble cells, have similar characteristics. These images, which occur in a variety of shapes, often show abnormalities in the organ or cell region. The convolution operation possesses…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

The uncertainty principle is a fundamental principle in theoretical physics, such as quantum mechanics and classical mechanics. It plays a prime role in signal processing, including optics, where a signal is to be analyzed simultaneously in…

In high-dimensional data processing and data analysis related to dual quaternion statistics, generalized singular value decomposition (GSVD) of a dual quaternion matrix pair is an essential numerical linear algebra tool for an elegant…

Following the idea of the fractional space-time Fourier transform, a linear canonical space-time transform for 16-dimensional space-time $C\ell_{3,1}$-valued signals is investigated in this paper. First, the definition of the proposed…

We propose the adaptive quadrature detection for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD scheme uses Gaussian subcarrier continuous variables for the information conveying and Gaussian…

Vision transformers have become popular as a possible substitute to convolutional neural networks (CNNs) for a variety of computer vision applications. These transformers, with their ability to focus on global relationships in images, offer…

We investigate the non-equilibrium four-vector work in an expanding relativistic piston. We derive the exact work distribution in this pedagogical model and find that the joint distribution of four-vector work $(W^0, W^1)$ concentrates on…

Neural network generalizability is becoming a broad research field due to the increasing availability of datasets from different sources and for various tasks. This issue is even wider when processing medical data, where a lack of…

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go,…

Vision transformers (ViTs) have found only limited practical use in processing images, in spite of their state-of-the-art accuracy on certain benchmarks. The reason for their limited use include their need for larger training datasets and…

We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner…

In this paper we show how the spectral theory based on the notion of $S$-spectrum allows us to study new classes of fractional diffusion and of fractional evolution processes. We prove new results on the quaternionic version of the…

In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…

Facial expression recognition (FER) is a challenging topic in artificial intelligence. Recently, many researchers have attempted to introduce Vision Transformer (ViT) to the FER task. However, ViT cannot fully utilize emotional features…

Quantum machine learning is receiving significant attention currently, but its usefulness in comparison to classical machine learning techniques for practical applications remains unclear. However, there are indications that certain quantum…

The correlator of vector and nonsinglet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of QCD vacuum. In general the correlator has two Lorentz structures: longitudinal w_L and…

We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…