Related papers: A Survey of Fusion Frames in Hilbert Spaces

The concept of a bi-g-fusion frame for a Hilbert space, which is a generalizations of a controlled g-fusion frame, is introduced and an example is given. Finally, bi-g-fusion frame in tensor product of Hilbert spaces is considered.

In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…

Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…

We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…

In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful…

We introduce the notion of a generalized fusion frame in quaternionic Hilbert space. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, we construct…

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.…

The fusion techniques that utilize multiple feature sets to form new features that are often more robust and contain useful information for future processing are referred to as feature fusion. The term data fusion is applied to the class of…

We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…

This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…

The present paper provides a comprehensive study of de-noising properties of frames and, in particular, tight frames, which constitute one of the most popular tools in contemporary signal processing. The objective of the paper is to bridge…

Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…

Just like the well-established Euler angles representation, fused angles are a convenient parameterisation for rotations in three-dimensional Euclidean space. They were developed in the context of balancing bodies, most specifically walking…

Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical…

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…

Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…

Vision Foundation Models (VFMs) have become the cornerstone of modern computer vision, offering robust representations across a wide array of tasks. While recent advances allow these models to handle varying input sizes during training,…

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…

In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…