Related papers: Frames and Finite Dimensionality: Frame Transforma…
The purpose of this note is to present a proof of the existence of Gabor frames in general linear position in all finite dimensions. The tools developed in this note are also helpful towards an explicit construction of such a frame, which…
Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with…
In this paper we define "piecewise scalable frames". This new scaling process allows us to alter many frames to Parseval frames which is impossible by the previous standard scaling. We give necessary and sufficient conditions for a frame to…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
Deep learning using Convolutional Neural Networks (CNNs) has been shown to significantly out-performed many conventional vision algorithms. Despite efforts to increase the CNN efficiency both algorithmically and with specialized hardware,…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We propose a novel and efficient, custom frame synchronization architecture aimed at rapid deployment on any hardware platform. Frame synchronization is the process of discerning valid data frames from an incoming transmission and in this…
For a given class ${\cal F}$ of uniform frames of fixed redundancy we define a Grassmannian frame as one that minimizes the maximal correlation $|< f_k,f_l >|$ among all frames $\{f_k\}_{k \in {\cal I}} \in {\cal F}$. We first analyze…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
Decision Boundary Maps (DBMs) are an effective tool for visualising machine learning classification boundaries. Yet, DBM quality strongly depends on the dimensionality reduction (DR) technique and high dimensional space used for the data…
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…
Autograd-based software packages have recently renewed interest in image registration using homography and other geometric models by gradient descent and optimization, e.g., AirLab and DRMIME. In this work, we emphasize on using complex…
Thye theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and much more, as well as being a fruitful area of research in abstract mathematics. In this…
Feature Structures (FSs) are a widespread tool used for decompositional frameworks of Attribute-Value associations. Even though they thrive in simple systems, they lack a way of representing higher-order entities and relations. This is…
This study investigates high-order face and edge elements in finite element methods, with a focus on their geometric attributes, indexing management, and practical application. The exposition begins by a geometric decomposition of Lagrange…
Using the 4th and the 3rd degree spherical harmonics as the representations for volumetric frames, we describe a simple algebraic technique for combining multiple frame orientation constraints into a single quadratic penalty function. This…
Matching two images while estimating their relative geometry is a key step in many computer vision applications. For decades, a well-established pipeline, consisting of SIFT, RANSAC, and 8-point algorithm, has been used for this task.…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…