Construction of robust frames in erasure recovery

Lv, Fusheng; Sun, Wei

doi:10.1016/j.laa.2015.04.017

Cited by 7 publications

(3 citation statements)

References 17 publications

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“…For example, in [13], the authors found the optimal dual frames that minimize the reconstruction error for 1-erasure and 2-erasures. Many other scholars have researched this issue in recent years, such as [14][15][16], and so on.…”

Section: Introductionmentioning

confidence: 99%

Erasure Recovery Matrices for Data Erasures and Rearrangements

He,

Wu,

Leng

2024

Mathematics

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When studying signal reconstruction, the frames are often selected in advance as encoding tools. However, in practical applications, this encoding frame may be subject to attacks by intermediaries and generate errors. To solve this problem, in this paper, the erasure recovery matrices for data erasures and rearrangements are analyzed. Unlike the previous research, first of all, we introduce a kind of frame and its erasure recovery matrix M so that MI,Λ=Im×m, where Im×m is a unit matrix. In this case, we do not need to invert the matrix of the frame operator and the erasure recovery matrix, and this greatly simplifies reconstruction problems and calculations. Then three different construction algorithms of the above erasure recovery matrix M and the frame are proposed, and each of them has advantages. Furthermore, some restrictions on M so that the constructed frame and erasure recovery matrix M can recover coefficients from rearrangements are imposed. We prove that in some cases, the above M and frame can recover coefficients stably from m rearrangements.

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Section: Introductionmentioning

confidence: 99%

Erasure Recovery Matrices for Data Erasures and Rearrangements

He,

Wu,

Leng

2024

Mathematics

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“…They also showed that every full spark frame can be rescaled to be an almost self-located frames or almost robust frames. In their work, 11 Lv and Sun give some explicit construction of almost self-located frames and almost robust frames.…”

Section: Introductionmentioning

confidence: 99%

“…The frames constructed in Lv and Sun and Han et al 11,12 contain irrational numbers. Considering the quantization errors in application, it is necessary to discuss the stability of the property of almost self-located robustness.…”

Section: Introductionmentioning

confidence: 99%

Perturbation and construction of almost self‐located robust frames with applications to erasure recovery

Zhen

Yang

Zheng

2021

Math Methods in App Sciences

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In the frame theory, stability is one of the most important properties of frames. In this paper, we investigate the stability of the almost self-located robust frames, which can reconstruct signals from its unordered partial frame coefficients. We give conditions on the stability of almost self-located robustness of frames in erasure recovery. We prove that the property of almost self-located robustness is preserved with respect to an invertible operator, and consequently, every almost self-robust frame can be transformed into an almost self-located robust Parseval frame by using a special invertible transformation. We also present some construction methods of almost self-located robust frames. In particular, we show that every frame can be rescaled to an almost self-located frame after adding a suitable vector.

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