本文選題：壓縮傳感 + 信號重構　； 參考：《燕山大學》2014年碩士論文

【摘要】：傳統(tǒng)的奈奎斯特采樣定理要求采樣信號的頻率必須大于或等于原始信號頻率的兩倍才能保證不失真的恢復出原始信號，這無疑給信號處理的能力提出了更高的要求，也給相應的硬件設備帶來了極大的挑戰(zhàn)。壓縮傳感理論突破了傳統(tǒng)的香農(nóng)采樣定理，以遠低于奈奎斯特采樣頻率的非適應性測量和優(yōu)化方法高概率重構信號。本文主要針對目前壓縮傳感重構算法在測量值數(shù)目和重建質(zhì)量上的一些不足進行了深入的研究并做出了一些改進。 首先，針對目前壓縮傳感理論的經(jīng)典重構算法進行了分析與仿真，主要包括基于l0范數(shù)最小化的貪婪系列算法和基于l1范數(shù)最小化的經(jīng)典算法，并且針對現(xiàn)有重構算法在對圖像進行處理時按列處理的缺陷，提出了一種行列均衡的改進方案，實驗證明該方案提高了重構質(zhì)量。 其次，針對目前CS重構中l(wèi)1范數(shù)優(yōu)化在某些測量值很少的情況下不能精確地重構出原始信號的不足，提出采用l p(0p1)范數(shù)代替l1范數(shù)，并且將參數(shù)規(guī)則化引入到算法中，提出了一種參數(shù)規(guī)則化的IRLS算法，實驗證明改進的算法提高了對稀疏信號的恢復能力。此外，針對所提算法在重構二維圖像時存儲量大、重構時間較長的缺點，將分塊思想引入到該算法中，提高了重構速度。 最后，針對目前無線傳感器網(wǎng)絡的能量有限性問題，提出將壓縮傳感應用于無線傳感器網(wǎng)絡中，實驗證明，CS與WSN的結合，，降低了網(wǎng)絡的能耗，延長了網(wǎng)絡的生命周期。
[Abstract]:The traditional Nyquist sampling theorem requires that the frequency of the sampled signal must be greater than or equal to twice the frequency of the original signal in order to guarantee the recovery of the original signal without distortion, which undoubtedly puts forward higher requirements for the ability of signal processing. It also brings great challenges to the corresponding hardware equipment. The compression sensing theory breaks through the traditional Shannon sampling theorem and uses the non-adaptive measurement and optimization method to reconstruct signals with high probability which is far lower than Nyquist sampling frequency. In this paper, the shortcomings of the current compression sensor reconstruction algorithm in the number of measured values and reconstruction quality are studied and some improvements are made. Firstly, the classical reconstruction algorithms of compression sensing theory are analyzed and simulated, including greedy series algorithms based on l0 norm minimization and classical algorithms based on L1 norm minimization. Aiming at the defects of the existing reconstruction algorithms in processing images by column, an improved scheme of row and column equalization is proposed, which is proved by experiments to improve the reconstruction quality. Secondly, aiming at the deficiency of L 1 norm optimization in CS reconstruction which can not accurately reconstruct the original signal in some cases where the measurement value is very small, this paper proposes to replace l 1 norm with l 1 norm by using l p0 p 1) norm, and introduces the parameter regularization into the algorithm. A parameterized IRLS algorithm is proposed. The experimental results show that the improved algorithm improves the recovery ability of sparse signals. In addition, in view of the disadvantages of the proposed algorithm, such as large storage and long reconstruction time, the proposed algorithm is introduced into the algorithm to improve the reconstruction speed. Finally, aiming at the problem of limited energy in wireless sensor networks at present, the application of compressed sensing in wireless sensor networks is proposed. Experiments show that the combination of CS and WSN reduces the energy consumption and prolongs the lifetime of wireless sensor networks.
【學位授予單位】：燕山大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.7

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