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It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…
Transceivers used for telecommunications transmit and receive specific modulation patterns that are represented as sequences of complex numbers. Classifying modulation patterns is challenging because noise and channel impairments affect the…
Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks…
Circular convolutions and the corresponding frequency domain formula are fundamentally important in image restoration; however, in this paper, we'll prove that the usual computing method of circular convolutions violates the physical…
With the use of deep learning in many areas, how to improve this technology or how to develop the structure used more effectively and in a shorter time is an issue that is of interest to many people working in this field. Many studies are…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
Different types of convolution operations involving large Vandermonde matrices are considered. The convolutions parallel those of large Gaussian matrices and additive and multiplicative free convolution. First additive and multiplicative…
The paper deals with the construction of images from visibilities acquired using aperture synthesis instruments: Fourier synthesis, deconvolution, and spectral interpolation/extrapolation. Its intended application is to specific situations…
Dictionary learning algorithms or supervised deep convolution networks have considerably improved the efficiency of predefined feature representations such as SIFT. We introduce a deep scattering convolution network, with predefined wavelet…
Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention,…
Usually, convolution refers to Laplace convolution in the literature. But Mellin convolutions can yield very ueeful results. This aspect is illustrated in the coming sections. This paper deals with Mellin convolutions of products and…
This report will explore and answer fundamental questions about taking Fourier Transforms and tying it with recent advances in AI and neural architecture. One interpretation of the Fourier Transform is decomposing a signal into its…
Convolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of Fourier masks applicable in the multiphoton Fourier space is identified. This concept…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
Transfer learning makes it possible to use large vision networks on a variety of domains, by specializing their models' general filters to new tasks. However, these networks assume the input images to have 3 input channels, making them…