Related papers: Probabilistic Modelled Optimal Frame for Erasures …
The prime focus of this paper is the study of optimal duals of a given finite frame as well as optimal dual pairs, in the context of probability modelled erasures of frame coefficients. We characterize optimal dual frames (and dual pairs)…
This paper investigates the optimization of dual frame pairs in the context of erasure problems in data transmission, using a graph theoretical approach. Frames are essential for mitigating errors and signal loss due to their redundancy…
This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and…
Finding the optimal dual frame and optimal dual pair for signal reconstruction, which can minimize the reconstruction error when erasure occurs during data transmission, is a deep rooted problem from the perspective of frame theory. In this…
In this paper, we investigates the problem of optimal dual frame selection for signal reconstruction in the presence of erasures. Unlike traditional approaches relying on left inverses, we evaluate performance through the norms of error…
The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality measure using the Frobenius norm of the error operator has been…
In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual for 1-erasure reconstruction. In this paper, we demonstrate…
The purpose of this work is to examine the structure of optimal dual fusion frames and get more exibility in the use of dual fusion frames for erasures of subspaces. We deal with optimal dual fusion frames with respect to different…
In [9], authors studied spectrally optimal dual frames for 1-erasure and 2-erasures of frames generated by graph. In this paper, we study spectrally optimal dual frames for r-erasures. We show that the spectral radius of the error operator…
In this paper we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased coefficients are indexed by a finite set $E$. Starting from a frame $(x_n)_{n=1}^\infty$ and its arbitrary dual frame, we…
In this paper we introduce a new probabilistic model for optimizing erasures occurring in data transmission using Parseval frames and a sequence of Bernoulli random variables associated to the channels of the transmission. We establish…
The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…
Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two…
Recently, the concept of frames generated by graphs has been introduced in \cite{D}. In this paper, we study spectrally optimal dual frames of frames generated by graphs. We show that if the frame is generated by a connected graph, then its…
Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…
We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…
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…
We propose a new approach to the problem of recovering signal from frame coefficients with erasures. Such problems arise naturally from applications where some of the coefficients could be corrupted or erased during the data transmission.…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of…