Related papers: New convolution related theorems and applications …
This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on…
High-numerical-aperture optical coherence tomography (OCT) enables sub-cellular imaging but faces a trade-off between lateral resolution and depth of focus. Computational refocusing can correct defocus in Fourier-domain OCT, yet its…
We analyze the emergence of correlated optical phenomena in the transmission of light through a waveguide that confines classical or ultracold quantum degenerate atomic ensembles. The conditions of the correlated collective response are…
Higher order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear wave guide and a nonlinear (quadratic) wave guide operated by second harmonic…
Recent work has highlighted several advantages of enforcing orthogonality in the weight layers of deep networks, such as maintaining the stability of activations, preserving gradient norms, and enhancing adversarial robustness by enforcing…
We compare analytic predictions for real and Fourier space two-point statistics for biased tracers from a variety of Lagrangian Perturbation Theory approaches against those from state of the art N-body simulations in $f(R)$ Hu-Sawicki and…
Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning…
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data…
We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a…
Kernelized Correlation Filter (KCF) is one of the state-of-the-art object trackers. However, it does not reasonably model the distribution of correlation response during tracking process, which might cause the drifting problem, especially…
We tackle the problems of latent variables identification and ``out-of-support'' image generation in representation learning. We show that both are possible for a class of decoders that we call additive, which are reminiscent of decoders…
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images.…
The quaternion offset linear canonical transform (QOLCT) which is time shifted and frequency modulated version of the quaternion linear canonical transform (QLCT) provides a more general framework of most existing signal processing tools.…
In this work we present an analogue of the inverse scattering for Canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the…
We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain…
In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and…
During the last years, Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in image classification. Their architectures have largely drawn inspiration by models of the primate visual system. However, while recent…
Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. However, most realizations are limited to classical systems and quantum fluctuations of light is unexplored. For the first…
Linear-optical circuits are elementary building blocks for classical and quantum information processing with light. In particular, due to its monolithic structure, integrated photonics offers great phase-stability and can rely on the large…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…