Related papers: Frames and Finite Dimensionality: Frame Transforma…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
The technique requires the epipolar geometry to be pre-estimated between each image pair. It exploits the constraints which the camera movement implies, in order to apply a closed-form correction to the parameters of the input affinities.…
In this paper, we will establish a general method of studying finite-dimensional normed spaces, and apply this method to classifying $3$-dimensional and $4$-dimensional normed spaces over a non-spherically complete field. For this purpose,…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential.…
We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…
We give a number of algorithms for constructing unitary matrices and tight frames with specialized properties. These were produced at the request of researchers at the Frame Research Center (www.framerc.org) to help with their research on…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize…
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
The concept of frames, initially introduced by Duffin and Schaeffer, gained substantial recognition decades later when Daubechies, Grossman, and Meyer highlighted its significance. Since then, frame theory has become a fundamental and…
We present a theory of finite frames for subspaces of $\mathbb{C}^N$ . The definition of a subspace frame is given and results analogous to those from frame theory for $\mathbb{C}^N$ are proven.
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…
In this paper we investigate encoding the bit-stream resulting from coarse Sigma-Delta quantization of finite frame expansions (i.e., overdetermined representations) of vectors. We show that for a wide range of finite-frames, including…
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and $\mathcal{E} =…