Related papers: New convolution related theorems and applications …
Optical coherence tomography (OCT) can provide high-resolution cross-sectional images for analyzing superficial plaques in coronary arteries. Commonly, plaque characterization using intra-coronary OCT images is performed manually by expert…
In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…
The Correlation Filter is an algorithm that trains a linear template to discriminate between images and their translations. It is well suited to object tracking because its formulation in the Fourier domain provides a fast solution,…
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal…
We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on $[0,T]$. Though the approach we use is well known in the literature, the conditions under which the CLT…
The scientific interest in studying high-energy transient phenomena in the Universe has largely grown for the last decade. Now, multiple ground-based survey projects have emerged to continuously monitor the optical (and multi-messenger)…
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on…
Dynamic Textures (DTs) are sequences of images of moving scenes that exhibit certain stationarity properties in time such as smoke, vegetation and fire. The analysis of DT is important for recognition, segmentation, synthesis or retrieval…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT).…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
Image orientation detection requires high-level scene understanding. Humans use object recognition and contextual scene information to correctly orient images. In literature, the problem of image orientation detection is mostly confronted…
This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). The algorithm is based on a recently introduced variational…
Image-matched nonseparable wavelets can find potential use in many applications including image classification, segmen- tation, compressive sensing, etc. This paper proposes a novel design methodology that utilizes convolutional neural net-…
The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some…
As a generalization of the two-dimensional Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics, signal and image processing. To reduce the digital…
A new formulation of lateral imaging process of point-scanning optical coherence tomography (OCT) and a new differential contrast method designed by using this formulation are presented. The formulation is based on a mathematical sample…
Optical coherence tomography (OCT) is a volumetric imaging modality that empowers clinicians and scientists to noninvasively visualize the cross-sections of biological samples. As the latest generation of its kind, Fourier-domain OCT…
We introduce a class of convolutional neural networks (CNNs) that utilize recurrent neural networks (RNNs) as convolution filters. A convolution filter is typically implemented as a linear affine transformation followed by a non-linear…
We present a general theory of optical coherence tomography (OCT), which synthesizes the fundamental concepts and implementations of OCT under a common 3D k-space framework. At the heart of this analysis is the Fourier diffraction theorem,…