【摘要】：本文主要研究基于稀疏表示的地震信號(hào)壓縮方法。對于地震學(xué)學(xué)者來說,地震數(shù)據(jù)的記錄是很寶貴的資料,通過這些數(shù)據(jù)可以很好地學(xué)習(xí)地震的規(guī)律。人類對于地震數(shù)據(jù)的記錄已經(jīng)有100多年的歷史,保存了大量的地震數(shù)據(jù),其壓縮是一個(gè)不得不考慮的問題。地震信號(hào)中存在著自相似性,針對這一特點(diǎn),通過學(xué)習(xí)的方法獲得過完備字典,并使用稀疏表示來解決地震信號(hào)的壓縮問題。本文結(jié)合地震信號(hào)本身特點(diǎn),從字典原子間的相干性和樣本之間的相似性這兩個(gè)角度出發(fā),研究提高字典表達(dá)能力的方法,主要工作有兩方面。第一種方法是通過減少字典原子間相干性來提高字典表達(dá)能力。合理降低字典原子間相干性,可以避免字典中出現(xiàn)相似的原子對,這樣字典原子數(shù)在有限的情況下可以有效提高字典的表達(dá)能力。本文在字典更新時(shí)將含有r緊框架Φ的約束項(xiàng)加入到優(yōu)化問題中,來平衡原子間相干性和字典對樣本的表達(dá)誤差,使得字典對地震信號(hào)的表達(dá)達(dá)到最佳效果。第二種方法考慮到訓(xùn)練樣本中的相似性。通過聚類和字典學(xué)習(xí)兩種手段結(jié)合,訓(xùn)練過完備字典。分段后的小段樣本之間有很多相似性,通過聚類的手段,將小段樣本進(jìn)行聚類,并計(jì)算各類樣本的權(quán)重系數(shù)。在優(yōu)化問題中賦予各類樣本相對應(yīng)的權(quán)重系數(shù),通過對目標(biāo)函數(shù)的變換,原優(yōu)化問題可以使用K-SVD算法解決。通過實(shí)驗(yàn),驗(yàn)證了以上兩種方法的字典在信號(hào)重構(gòu)時(shí)的有效性。在傳統(tǒng)的字典學(xué)習(xí)模型基礎(chǔ)上,分別考慮字典原子間相干性以及樣本間相似性這兩個(gè)因素,從兩個(gè)方向改進(jìn)了字典學(xué)習(xí)模型,提高了字典的表達(dá)能力。在同等壓縮比的條件下,地震信號(hào)重構(gòu)效果得到提高。
[Abstract]:This paper mainly studies the seismic signal compression method based on sparse representation. For seismologists, the records of seismic data are very valuable data, through which the rules of earthquakes can be well learned. The records of seismic data have been recorded for more than 100 years, and a large number of seismic data have been preserved. The compression of seismic data is a problem that must be considered. There is self-similarity in seismic signals. According to this characteristic, the over-complete dictionary is obtained by means of learning, and sparse representation is used to solve the compression problem of seismic signals. In this paper, based on the characteristics of seismic signals and from the point of view of the coherence between atoms and the similarity between samples, the methods to improve the expression ability of dictionaries are studied. The main work is in two aspects. The first method is to improve the dictionary expression ability by reducing the interatomic coherence of dictionaries. A reasonable reduction of the coherence between dictionaries can avoid the occurrence of similar pairs of atoms in dictionaries, so that the number of atoms in dictionaries can effectively improve the expression ability of dictionaries under the condition that the number of atoms in dictionaries is limited. In this paper, the constraint with r-compact frame 桅 is added to the optimization problem when the dictionary is updated to balance the interatomic coherence and the expression error of the dictionary to the sample, so that the dictionary can get the best effect on the expression of seismic signals. The second method takes into account the similarity in training samples. Through the combination of clustering and dictionary learning, a complete dictionary has been trained. There are many similarities between the segmented samples. By means of clustering, the small segments of the samples are clustered and the weight coefficients of all kinds of samples are calculated. In the optimization problem, the corresponding weight coefficients are given to all kinds of samples. By transforming the objective function, the original optimization problem can be solved by using the K-SVD algorithm. The experimental results show that the dictionary of the above two methods is effective in signal reconstruction. Based on the traditional dictionary learning model, considering the coherence between atoms and the similarity between samples, the dictionary learning model is improved in two directions, and the dictionary expression ability is improved. Under the condition of the same compression ratio, the effect of seismic signal reconstruction is improved.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：P315.6

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