利用振幅資訊之單一位元壓縮式感測 應用於分散式參數估計技術

本碩士論文是壓縮式感測(Compressive Sensing, CS)應用於無線感測網路 (Wireless Sensor Network, WSN)上的一個研究，讓壓縮式感測使用量化過的量測值來估計原始的稀疏訊號。壓縮式感測是一項很常應用於無線感測網路中的技術，藉以對抗其實際環境的嚴苛限制。然而，感測值在傳送前一定要經過量化才可以以數位傳輸的方式傳送，然而量化的步驟隨著量化的複雜度越高而越耗能的。為了節省資源，發展至今，甚至使每個量測值經過量化器後只被配與一個位元來代表唯二的代表值。而使壓縮式感測利用被二元量化後的量測值來估計原始稀疏訊號，稱單一位元之壓縮式感測(1-Bit CS)。在本碩士論文中，我們探討將單一位元之壓縮式感測應用在有雜訊的無線感測網路上，並且各個傳送端將其位元送到中央接收端時會有位元翻轉的可能。於是我們提出了一套以振幅的資訊來輔助重建原訊號的方法，可分成兩個部分：1. 設計量化代表點，使中央接收端得到的量測值，因為量測雜訊、量化誤差以及位元翻轉的均方誤差能夠達到最小。2. 中央接收端將得到的量測值經過專門重建稀疏向量的最小化的重建方法 ( -Minimization Method)來估計原稀疏向量。在最後得到與量化代表點、原始訊號、量測雜訊以及位元翻轉機率有關的均方誤差式子，並且可以得到以閉合型式解的最佳均方誤差量化代表點。在模擬中可觀察到，我們所提出的方法可在感測時的訊號雜訊比較低以及感測器數目較少的時候，比現行很多專門設計給單一位元之壓縮式感測的疊代重建方法有更高的準確度。

關鍵字

壓縮式感測；量化；無線感測網路

並列摘要

One-bit compressive sensing (CS) is known to particularly suited for resource-constrained wireless sensor networks (WSNs). In this paper, we consider 1-bit CS over noisy WSNs subject to channel-induced bit flipping errors, and propose an amplitude-aided signal reconstruction scheme, by which (i) the representation points of local binary quantizers are designed to minimize the loss of data fidelity caused by local sensing noise, quantization, and bit sign flipping, and (ii) the FC adopts the conventional -minimization method for sparse signal recovery using the decoded and de-mapped binary data. The representation points of binary quantizers are designed by minimizing the mean square error (MSE) of the net data mismatch, taking into account the distributions of the nonzero signal entries, local sensing noise, quantization error, and bit flipping; a simple closed-form solution is then obtained. Numerical simulations show that our method improves the estimation accuracy when SNR is low or the number of sensors is small, as compared to state-of-the-art 1-bit CS algorithms relying solely on the sign message for signal recovery.

並列關鍵字

Compressive Sensing ； Quantization ； Wireless Sensor Networks

參考文獻

[1] R. G. Baraniuk, “Compressive sensing,” IEEE Signal Processing Magazine, vol. 24, no. 4, pp, 118-124, July 2007.

[5] L. Jacques, J. N. Laska, P. T. Boufounos and R. G. Baraniuk, "Robust 1-bit compressive sensing via binary stable embedding of sparse vectors," IEEE Trans. Information Theory, vol. 59, no. 4, pp. 2082-2202, April 2013.

[6] M. Yan, Y. Yang, and s. Osher, "Robust 1-bit compressive sensing using adaptive outlier pursuit," IEEE Trans. Signal Processing, vol. 60, no. 7, pp. 3868-3875, July 2012.

[7] A. Movahed, A. Panahi, and G. Durisi, "A robust RFPI-based 1-bit compressive sensing recovery algorithm," Proc. IEEE Information Theory Workshop, 2012, pp. 567-571.

[9] A. Y. Yang, M. Gastpar, R. Bajcsy, and S. S. Sastray, "Distributed sensor perception via sparse representation," Proc. of the IEEE, vol. 98, no., 6, pp. 1077-1088, June 2010.

國際替代計量

利用振幅資訊之單一位元壓縮式感測應用於分散式參數估計技術

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