相关论文: Frames, Graphs and Erasures

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…

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…

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…

Error occurs in data transmission process when some data are missing at the time of reconstruction. Finding the best dual frame or a dual pair that minimizes the reconstruction error when erasure occurs,is a deep-rooted problem in frame…

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.…

Data erasure can often occur in communication. Guarding against erasures involves redundancy in data representation. Mathematically this may be achieved by redundancy through the use of frames. One way to measure the robustness of a frame…

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…

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 [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…

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)…

A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…

We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…

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…

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…

We give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate…

In this work we continue the study of a new class of codes, called \emph{codes over graphs}. Here we consider storage systems where the information is stored on the edges of a complete directed graph with $n$ nodes. The failure model we…

This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other…

Erasures are a common problem that arises while signals or data are being transmitted. A profound challenge in frame theory is to find the optimal dual frames ($OD$-frames) to minimize the reconstruction error if erasures occur. In this…

We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter…

This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection…