| 摘要(英) |
In compressive sensing (CS) technology, the goal is to reconstruct the original signal using a sampling rate lower than the Shannon-Nyquist rate. To conserve resources and enhance data processing efficiency, we discuss 1-bit Compressive Sensing (1-bit CS) further. 1-bit CS is characterized by representing each measurement with only a single bit.
In this thesis, we construct a 1-bit CS system model and consider the occurrence of bit-flipping error during the sensing and transmission processes. This condition is commonly encountered in real-world scenarios and has a significant impact on existing reconstruction methods. Bit-flipping significantly impacts existing reconstruction methods. Based on this, we investigate whether it is possible to obtain additional information that aids reconstruction under the condition of limited information at the receiver. We improve existing reconstruction methods by proposing a concept on estimating the support of the original signal. Before reconstructing the signal, we first locate the support of the original signal and then reconstruct the signal based on these positions, effectively reducing the difference between the support of the estimated signal and the original signal.
When the support of the estimated signal is accurate and improves reconstruction performance, we further explore whether prior knowledge of the number of non-zero values in the original signal is necessary. In cases where the number of non-zero values in the original signal is unknown, we use statistical analysis to differentiate estimated values between zero and non-zero positions, determining whether they belong to the support. The results indicate that the greater the difference between the estimated values of zero and non-zero positions, the more accurate the judgment of the support. We integrate the obtained support information into existing methods to achieve more precise signal reconstruction. Compared to existing methods, the proposed approach not only provides more accurate reconstruction results but also significantly enhances resistance to bit-flipping error. Additionally, it meets the demands of real-world applications better. |
| 參考文獻 |
[1] Emmanuel J. Candes and Michael B. Wakin, “An Introduction To Compressive Sampling” IEEE Signal Processing Magazine, pp. 21-30, Mar. 2008
[2] E. Candes, The Restricted Isometry Property and its Implications for Compressed Sensing. Paris, France: C.R. Acad. Sci., 2008, vol. 3406, pp. 589–592, ser. I.
[3] Justin Romberg, “Imaging via Compressive Sampling” IEEE Signal Processing Magazine, pp. 14-20, Mar. 2008
[4] 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. Inf. Theory, vol. 59, no. 4, pp. 2082–2202, Apr. 2013.
[5] M. Yan, Y. Yang, and S. Osher, “Robust 1-bit compressive sensing using adaptive outlier pursuit,” IEEE Trans. Signal Process., vol. 60, no. 7, pp. 3868–3875, Jul. 2012.
[6] A. Movahed, A. Panahi, and G. Durisi, “A robust RFPI-based 1-bit compressive sensing recovery algorithm,” in Proc. IEEE Inf. Theory Workshop, pp. 567–571, 2012.
[7] Sivakant Gopi, Praneeth Netrapalli, Prateek Jain and Aditya Nori, “One-bit compressed sensing: Provable support and vector recovery,” International Conference on Machine Learning, pp. 154–162, 2013. |
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