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We demonstrate, in the full vector formulation of electromagnetic fields, that the well-known optical theorem pertinent for the characterization of a scatterer's extinction power and associated cross section can be expressed in a multitude…

Optics · Physics 2025-06-11 Edwin A. Marengo , Mohammadrasoul Taghavi

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are…

Numerical Analysis · Mathematics 2016-04-19 Peter Elbau , Leonidas Mindrinos , Otmar Scherzer

A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their…

Signal Processing · Electrical Eng. & Systems 2018-08-29 Julien Flamant , Pierre Chainais , Nicolas Le Bihan

In this paper, we propose a set of transform-based neural network layers as an alternative to the $3\times3$ Conv2D layers in Convolutional Neural Networks (CNNs). The proposed layers can be implemented based on orthogonal transforms such…

Computer Vision and Pattern Recognition · Computer Science 2024-04-24 Hongyi Pan , Emadeldeen Hamdan , Xin Zhu , Salih Atici , Ahmet Enis Cetin

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…

Mathematical Physics · Physics 2007-05-23 Gerald Kaiser

Convolution system is linear and time invariant, and can describe the optical imaging process. Based on convolution system, many deconvolution techniques have been developed for optical image analysis, such as boosting the space resolution…

Image and Video Processing · Electrical Eng. & Systems 2017-12-01 Song Yizhi , Xu Cheng , Ding Daoxin , Zhou Hang , Quan Tingwei , Li Shiwei

A theoretical description of local absorption is proposed in order to investigate spectral variations on a length scale comparable with the extension of the relevant quantum states. A general formulation is derived within the density-matrix…

Materials Science · Physics 2009-10-31 O. Mauritz , G. Goldoni , F. Rossi , E. Molinari

This work compares two tomographic imaging technologies, time-domain full-field optical coherence tomography (FFOCT) working in reflection and optical transmission tomography (OTT), using a new optical setup that combines both. We show…

Optical Coherence Tomography (OCT) has become an indispensable tool for investigating mesoscopic features in soft matter and fluid mechanics. Its ability to provide high-resolution, non-invasive measurements in both spatial and temporal…

Humans understand a set of canonical geometric transformations (such as translation and rotation) that support generalization by being untethered to any specific object. We explore inductive biases that help a neural network model learn…

Computer Vision and Pattern Recognition · Computer Science 2020-11-18 Zachary Dulberg , Jonathan Cohen

A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…

Quantum Physics · Physics 2021-02-03 Ding Jia

This note introduces a new family of wavelets and a multiresolution analysis, which exploits the relationship between analysing filters and Floquet's solution of Mathieu differential equations. The transfer function of both the detail and…

Methodology · Statistics 2015-01-29 M. M. S. Lira , H. M. de Oliveira , R. J. Cintra

As the availability of imagery data continues to swell, so do the demands on transmission, storage and processing power. Processing requirements to handle this plethora of data is quickly outpacing the utility of conventional processing…

Computer Vision and Pattern Recognition · Computer Science 2022-11-01 Artyom M. Grigoryan , Sos S. Agaian , Karen Panetta

The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing. Many areas of science and…

Machine Learning · Computer Science 2019-04-23 Taco Cohen , Mario Geiger , Jonas Köhler , Max Welling

The convolution layer has been the dominant feature extractor in computer vision for years. However, the spatial aggregation in convolution is basically a pattern matching process that applies fixed filters which are inefficient at modeling…

Computer Vision and Pattern Recognition · Computer Science 2019-04-26 Han Hu , Zheng Zhang , Zhenda Xie , Stephen Lin

Optical materials with special optical properties are widely used in a broad span of technologies, from computer displays to solar energy utilization leading to large dataset accumulated from years of extensive materials synthesis and…

Materials Science · Physics 2020-11-26 Rongzhi Dong , Yabo Dan , Xiang Li , Jianjun Hu

Orthogonal convolutional layers are valuable components in multiple areas of machine learning, such as adversarial robustness, normalizing flows, GANs, and Lipschitz-constrained models. Their ability to preserve norms and ensure stable…

Artificial Intelligence · Computer Science 2025-06-05 Thibaut Boissin , Franck Mamalet , Thomas Fel , Agustin Martin Picard , Thomas Massena , Mathieu Serrurier

Under the introduction of any interface in its trajectory, an optical beam experiences polarization-dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam…

The development of optical nanofibers (ONF) and the study and control of their optical properties when coupling atoms to their electromagnetic modes has opened new possibilities for their use in quantum optics and quantum information…

With the improvement of computer performance and the increase of data volume, the object detection based on convolutional neural network (CNN) has become the main algorithm for object detection. This paper summarizes the research progress…

Computer Vision and Pattern Recognition · Computer Science 2020-07-28 Wei Zhang , Zuoxiang Zeng