This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination of the elements in the original frame. Several examples are considered, such as a Fourier frame on a spiral. The procedure can be applied to the construction...

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

We consider perturbation of frames and frame sequences in a Hilbert space H. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation of the canonical dual of the original one and estimate the error in the approximation of functions belonging to the perturbed space. We then construct perturbations of ...

In this paper a novel method for machine-based black and white films colorization is presented. The kernel of the proposed scheme is a trained artificial neural network which maps the frame pixels from a grayscale space into a color space. We employ the texture coding method to capture the line/texture characteristics of each pixel as its most significant gray scale space feature, and using tha...

This is a short introduction to Hilbert space frame theory and its applications for those outside the area who want an introduction to the subject. We will increase this over time. There are incomplete sections at this time. If anyone wants to add a section or fill in an incomplete section on ”their applications” contact Pete Casazza. 1. Basic Definitions For a more complete treatment of frame ...

The main objective of this study was to determine how manipulating the amount of sensory information available about the body and surrounding environment influenced freezing of gait (FOG), while walking through a doorway. It was hypothesized that the more limited the sensory information, the greater the occurrence of freezing of gait. Nineteen patients with Parkinsoǹs disease who experience fre...

Equiform geometry is considered an extension of other geometries. Furthermore, equiform frame a generalization the Frenet frame. In this study, we begin by defining term “equiform parameter (EQP)”, frame”, and formulas (EQF)” in regard to Minkowski three-space. Second, define spacelike normal curves (SPN) three-space present variety descriptions these with (EQS) or timelike (EQN) principal norm...