本文選題：壓縮感知 + 稀疏�。� 參考：《吉林大學(xué)》2015年碩士論文

【摘要】：地震數(shù)據(jù)由于受到采集環(huán)境以及預(yù)處理等影響，往往會呈現(xiàn)不規(guī)則分布，這對地震數(shù)據(jù)的后期處理將產(chǎn)生不良影響。而基于壓縮感知理論的重構(gòu)方法能有效地恢復(fù)重構(gòu)地震數(shù)據(jù)，提高分辨率。 在傳統(tǒng)的地震數(shù)據(jù)采集過程中，由于受到奈奎斯特采樣定理的制約，地震數(shù)據(jù)的采集和存儲需要更高的要求，這為地震勘探的發(fā)展帶來了巨大的挑戰(zhàn)。近些年發(fā)展起來的壓縮感知（Compressive Sensing，CS）理論突破了奈奎斯特采樣定理的限制。它表明，如果待處理的不完整數(shù)據(jù)本身是稀疏的，或者在某個(gè)變換域內(nèi)是稀疏的，那么就有可能恢復(fù)重構(gòu)出符合一定精度要求的完整數(shù)據(jù)。 通常情況下，地震數(shù)據(jù)并不是稀疏的，但是可以找到一種稀疏變換域使其在該變換域內(nèi)稀疏。傅里葉變換能將地震數(shù)據(jù)由時(shí)間-空間域轉(zhuǎn)換到頻率-波數(shù)域，它是一種比較有效的稀疏表示方法，為基于壓縮感知理論的重構(gòu)方法提供了理論前提條件。 基于傅里葉變換的迭代閾值收縮算法是地震數(shù)據(jù)重構(gòu)過程中比較常用的一種方法，但是傳統(tǒng)的迭代閾值算法收斂速度較慢，降低了運(yùn)算效率。本文基于壓縮感知理論，引用了圖像處理中的一種基于L1范數(shù)的迭代線性擴(kuò)展閾值算法來解決地震數(shù)據(jù)重構(gòu)問題。它不是直接通過最小化目標(biāo)函數(shù)來估算重構(gòu)數(shù)據(jù)，而是把這個(gè)過程參數(shù)化為一些基本閾值函數(shù)的線性組合，并通過最小化目標(biāo)函數(shù)來求取線性加權(quán)系數(shù)，然后在迭代過程中更新該閾值函數(shù)。該算法的主要優(yōu)勢體現(xiàn)在每次只需要通過求解線性系數(shù)來解決這個(gè)優(yōu)化問題。當(dāng)基本的閾值函數(shù)滿足一定的約束條件時(shí)，就能夠保證這種算法的全局收斂性。同時(shí)，根據(jù)兩步迭代閾值收縮算法能夠加快收斂速度，本文也給出了基于兩步迭代的線性閾值擴(kuò)展算法的原理和流程，并將該算法與傳統(tǒng)的迭代閾值算法進(jìn)行了對比分析，，表明了該算法具有更快的收斂速度。 理論模型和實(shí)際處理的結(jié)果表明，迭代線性擴(kuò)展閾值算法不僅能有效地用于解決地震數(shù)據(jù)重構(gòu)問題，并且擁有較好的抗噪能力，同時(shí)具備收斂速度較快的優(yōu)點(diǎn)。
[Abstract]:Due to the influence of acquisition environment and preprocessing, seismic data often presents irregular distribution, which will have a negative impact on the post-processing of seismic data. The reconstruction method based on compression sensing theory can effectively restore reconstructed seismic data and improve resolution. In the process of traditional seismic data acquisition, because of the restriction of Nyquist sampling theorem, the acquisition and storage of seismic data need higher requirements, which brings great challenges to the development of seismic exploration. In recent years, compressed sensing theory has broken through the limitation of Nyquist sampling theorem. It shows that if the incomplete data to be processed is sparse itself or is sparse in a transform domain, it is possible to restore and reconstruct the complete data that meets the requirements of certain precision. In general, seismic data is not sparse, but a sparse transform domain can be found to make it sparse in that domain. Fourier transform can transform seismic data from time-space domain to frequency-wavenumber domain. It is an effective sparse representation method and provides a theoretical prerequisite for reconstruction method based on compression perception theory. Iterative threshold shrinkage algorithm based on Fourier transform is a commonly used method in seismic data reconstruction, but the traditional iterative threshold algorithm converges slowly and reduces the operation efficiency. Based on the theory of compression perception, an iterative linear extended threshold algorithm based on L1 norm in image processing is introduced to solve the problem of seismic data reconstruction. Instead of directly estimating the reconstructed data by minimizing the objective function, it converts the process parameter into a linear combination of some basic threshold functions, and obtains the linear weighting coefficient by minimizing the objective function. The threshold function is then updated during the iteration. The main advantage of the algorithm is that it only needs to solve the optimization problem by solving the linear coefficients at a time. The global convergence of the algorithm can be guaranteed when the basic threshold function satisfies certain constraints. At the same time, according to the two-step iterative threshold shrinkage algorithm can accelerate the convergence rate, this paper also gives the principle and flow of the linear threshold expansion algorithm based on two-step iteration, and compares the algorithm with the traditional iterative threshold algorithm. It shows that the algorithm has faster convergence speed. The theoretical model and practical processing results show that the iterative linear extended threshold algorithm can not only effectively solve the seismic data reconstruction problem, but also has a good anti-noise ability, and has the advantage of faster convergence speed.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：P631.44

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 高建軍;陳小宏;李景葉;劉國昌;馬劍;;基于POCS方法指數(shù)閾值模型的不規(guī)則地震數(shù)據(jù)重建(英文)[J];Applied Geophysics;2010年03期

2 吳招才;劉天佑;;地震數(shù)據(jù)去噪中的小波方法[J];地球物理學(xué)進(jìn)展;2008年02期

3 石光明;劉丹華;高大化;劉哲;林杰;王良君;;壓縮感知理論及其研究進(jìn)展[J];電子學(xué)報(bào);2009年05期

4 余慧敏;方廣有;;壓縮感知理論在探地雷達(dá)三維成像中的應(yīng)用[J];電子與信息學(xué)報(bào);2010年01期

5 王艷;練秋生;李凱;;基于聯(lián)合正則化及壓縮傳感的MRI圖像重構(gòu)[J];光學(xué)技術(shù);2010年03期

6 劉財(cái);李鵬;劉洋;王典;馮fE;劉殿秘;;基于seislet變換的反假頻迭代數(shù)據(jù)插值方法[J];地球物理學(xué)報(bào);2013年05期

7 黃捍東;張如偉;郭迎春;;地震信號的小波分頻處理[J];石油天然氣學(xué)報(bào);2008年03期

8 戴瓊海;付長軍;季向陽;;壓縮感知研究[J];計(jì)算機(jī)學(xué)報(bào);2011年03期

9 許郡;;基于DCT與DWT的水印算法的比較分析[J];南通航運(yùn)職業(yè)技術(shù)學(xué)院學(xué)報(bào);2009年03期

10 程冰潔;徐天吉;;地震信號的多尺度頻率與吸收屬性[J];新疆石油地質(zhì);2008年03期

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