本文選題：壓縮感知 + 重構(gòu)算法��； 參考：《湘潭大學(xué)》2017年碩士論文

【摘要】：隨著科技的進(jìn)步,大量的傳感器被投入使用,而這些設(shè)備采用奈奎斯特定理采樣雖然對信號可實(shí)現(xiàn)精確重構(gòu),但是帶來海量的數(shù)據(jù)采集、傳輸和存儲,且奈奎斯特采樣定理依賴信號的帶寬。壓縮感知的提出突破奈奎斯特采樣定理的限制,不依賴信號的帶寬,而是基于信號的稀疏性。壓縮感知重構(gòu)算法是壓縮感知中尤為重要的部分,本文致力于優(yōu)化壓縮感知重構(gòu)算法,提升算法的重構(gòu)性能,提出一種平滑L0范數(shù)最小化的迭代重構(gòu)算法和一種分布式壓縮感知中自適應(yīng)閾值迭代重構(gòu)算法。本文的主要研究工作如下:提出一種平滑L0范數(shù)的迭代重構(gòu)算法。一種平滑L0范數(shù)的迭代重構(gòu)算法是一種復(fù)雜度較低,高準(zhǔn)確率的重構(gòu)方法。首先,在平滑L0范數(shù)上,本文采樣兩種函數(shù)逼近L0范數(shù),求解平滑L0范數(shù)問題,采用梯度下降方法,得到迭代公式,在每一步迭代中,計(jì)算迭代公式,得到迭代結(jié)果,獲取其對應(yīng)的支撐集,采用支撐集對迭代結(jié)果進(jìn)行修正,使得殘差更小。當(dāng)達(dá)到迭代停止條件,則停止迭代過程。相比于對比算法,該方法可達(dá)到更高的重構(gòu)精度,同時其復(fù)雜度相對較低,對二維Lena圖像進(jìn)行重構(gòu)時,在不同的采樣率的情況下,本文提出的方法在采樣率較低的情況下,重構(gòu)信號的PSNR明顯高于其他的對比算法,存在著明顯的優(yōu)勢。提出一種分布式壓縮感知中自適應(yīng)閾值迭代重構(gòu)算法,針對網(wǎng)絡(luò)模型中,在分布式的場景下,采用分布式壓縮感知的信號模型建模,該方法是一種分散式并行算法。假設(shè)網(wǎng)絡(luò)中的節(jié)點(diǎn)本身具有一定的計(jì)算能力,每個節(jié)點(diǎn)將自身重構(gòu)的支撐集發(fā)送給周圍節(jié)點(diǎn),節(jié)點(diǎn)收到周圍節(jié)點(diǎn)的支撐集,對支撐集進(jìn)行融合操作,最終反饋給周圍的節(jié)點(diǎn),多次信息交互后,即可得到正確的支撐集。該方法不僅有效減少網(wǎng)絡(luò)中數(shù)據(jù)量的傳遞,采用并行的算法,重構(gòu)速度更快。實(shí)驗(yàn)表明,該算法應(yīng)用于有信號噪聲的無線網(wǎng)絡(luò)中,能完美重構(gòu)出原始信號。
[Abstract]:With the development of science and technology, a large number of sensors have been put into use, and these devices use Nyquist theorem sampling, although the signal can be accurately reconstructed, but it brings massive data acquisition, transmission and storage. The Nyquist sampling theorem depends on the bandwidth of the signal. Compression sensing is proposed to break through the Nyquist sampling theorem, which does not depend on the bandwidth of the signal, but based on the sparsity of the signal. Compression sensing reconstruction algorithm is an important part of compression perception. This paper is devoted to optimizing the compression perception reconstruction algorithm to improve the performance of the algorithm. An iterative reconstruction algorithm with smooth L0 norm minimization and an adaptive threshold iterative reconstruction algorithm in distributed compression perception are proposed. The main work of this paper is as follows: an iterative reconstruction algorithm with smooth L 0 norm is proposed. An iterative reconstruction algorithm with smooth L0 norm is a low complexity and high accuracy reconstruction method. First of all, on the smooth L0 norm, we sample two functions to approximate the L0 norm and solve the smooth L0 norm problem. The gradient descent method is used to obtain the iterative formula. In each step of iteration, the iterative formula is calculated and the iterative result is obtained. The corresponding support set is obtained, and the iterative result is modified by the support set, which makes the residual error smaller. When the iterative stop condition is reached, the iterative process is stopped. Compared with the contrast algorithm, this method can achieve higher reconstruction accuracy, and its complexity is relatively low. In the case of different sampling rates, the method proposed in this paper has a lower sampling rate when the two-dimensional Lena image is reconstructed. The PSNR of reconstructed signal is obviously higher than that of other contrast algorithms, and it has obvious advantages. An adaptive threshold iterative reconstruction algorithm for distributed compression awareness is proposed. In the network model, a distributed compression sensing signal model is used to model the network model. This method is a decentralized parallel algorithm. Assuming that the nodes in the network have a certain computational power, each node sends its reconstructed support set to the surrounding node, and the node receives the support set of the surrounding node, and fuses the support set to the surrounding node, and finally feeds back to the surrounding node. After many information exchanges, the correct support set can be obtained. This method not only effectively reduces the data transfer in the network, but also uses parallel algorithm, so the reconstruction speed is faster. Experimental results show that the proposed algorithm can reconstruct the original signal perfectly in wireless networks with signal noise.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN911.7

【參考文獻(xiàn)】

相關(guān)期刊論文 前8條

1 齊煥芳;徐源浩;;用于壓縮感知信號重建的SL_0改進(jìn)算法[J];電子科技;2015年04期

2 荊楠;畢衛(wèi)紅;胡正平;王林;;動態(tài)壓縮感知綜述[J];自動化學(xué)報(bào);2015年01期

3 王強(qiáng);李佳;沈毅;;壓縮感知中確定性測量矩陣構(gòu)造算法綜述[J];電子學(xué)報(bào);2013年10期

4 楊良龍;趙生妹;鄭寶玉;唐文娟;;基于SL0壓縮感知信號重建的改進(jìn)算法[J];信號處理;2012年06期

5 趙瑞珍;林婉娟;李浩;胡紹海;;基于光滑l_0范數(shù)和修正牛頓法的壓縮感知重建算法[J];計(jì)算機(jī)輔助設(shè)計(jì)與圖形學(xué)學(xué)報(bào);2012年04期

6 ;Generating dense and super-resolution ISAR image by combining bandwidth extrapolation and compressive sensing[J];Science China(Information Sciences);2011年10期

7 何楚;劉明;馮倩;鄧新萍;;基于多尺度壓縮感知金字塔的極化干涉SAR圖像分類[J];自動化學(xué)報(bào);2011年07期

8 蔡騁;張明;朱俊平;;基于壓縮感知理論的雜草種子分類識別[J];中國科學(xué):信息科學(xué);2010年S1期

，

本文編號：1800732