Related papers: Optimal Dual Frame Pairs: A Synergy with Graph The…
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…
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…
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)…
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…
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…
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…
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…
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…
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…
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 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…
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.…
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…
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 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…
In this paper, we give simple optimal lower bounds on the one-way two-party communication complexity of approximate Maximum Matching and Minimum Vertex Cover with deletions. In our model, Alice holds a set of edges and sends a single…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
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…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…