本文關(guān)鍵詞：基于改進(jìn)閾值函數(shù)的小波去噪及其優(yōu)化研究　出處：《昆明理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 小波變換 小波基 分解層數(shù) 閾值函數(shù) 粒子群優(yōu)化算法

【摘要】：在計(jì)算機(jī)控制系統(tǒng)中,信號(hào)的傳輸、檢測(cè)和采集等受到環(huán)境影響而遭到不同程度隨機(jī)噪聲污染,對(duì)此實(shí)行信號(hào)去噪十分必要。如何濾除實(shí)際信號(hào)中的噪聲,并獲取有用信號(hào),是目前研究熱點(diǎn)。特別是高頻部分和強(qiáng)噪聲相混疊信號(hào)、微弱信號(hào)或非平穩(wěn)隨機(jī)信號(hào),傳統(tǒng)處理平穩(wěn)信號(hào)的傅里葉變換對(duì)這些信號(hào)不能局部分析,而小波變換擁有時(shí)頻局部分析能力,對(duì)以上信號(hào)去噪效果相對(duì)較好,其應(yīng)用也極為廣泛。幾類小波去噪方法里,小波閾值收縮去噪法可以在最小均方誤差意義上接近最優(yōu),且擁有很好視覺成效,而受到及廣的運(yùn)用與深層次的研究。在小波閾值去噪方法里面,小波基、分解層數(shù)、閾值和閾值函數(shù)是小波閾值去噪的重要性因素。對(duì)各種含噪信號(hào)的處理,不一樣的小波基具有著不一樣的特點(diǎn),可以十分確信的是:往往沒有一種小波基函數(shù)能夠針對(duì)所有類型的信號(hào)都獲得最優(yōu)的去噪效果。同時(shí),對(duì)于分解層數(shù)來說,也可以十分確定的是:不相同的信號(hào)、不相同的信噪比下會(huì)對(duì)應(yīng)著一種去噪效果較佳或接近最佳的分解層數(shù)。本文針對(duì)小波基函數(shù)和分解層數(shù)的確定創(chuàng)造出一個(gè)算法,能夠針對(duì)待處理的信號(hào)做出分析,以信噪比為指標(biāo),算法通過計(jì)算采用不同的小波基函數(shù)或分解層數(shù)對(duì)待處理的含噪信號(hào)處理之后的信噪比改善量,得出其關(guān)系模型以確定最適當(dāng)?shù)男〔ɑ瘮?shù)和分解層數(shù)。閾值函數(shù)的選取直接影響信號(hào)重構(gòu)精確度,而對(duì)于先前的硬、軟閾值函數(shù)擁有的一定缺點(diǎn):硬閾值函數(shù)曲線在閾值處是不連續(xù)的,這種擁有間斷點(diǎn)的現(xiàn)象會(huì)促使去噪之后重構(gòu)信號(hào)更輕易發(fā)生附加的振蕩,造成“偽吉布斯”現(xiàn)象,并且大于閾值的小波系數(shù)中也通常染雜著噪聲的擾動(dòng),影響了最后重構(gòu)信號(hào)的質(zhì)量;軟閾值函數(shù)也有自己的缺陷:在進(jìn)行閾值處理時(shí),當(dāng)小波系數(shù)的絕對(duì)值大于或者等于此閾值時(shí),直接采取了將小波系數(shù)都減去了閾值這個(gè)辦法,這樣會(huì)造成小波的估計(jì)系數(shù)和原來信號(hào)的小波系數(shù)兩者具有一定的偏差,會(huì)很大程度上影響最后信號(hào)重構(gòu)的效果。針對(duì)傳統(tǒng)閾值函數(shù)的缺點(diǎn),許多學(xué)者提出了在軟、硬閾值中間的改進(jìn)型閾值函數(shù)算法。但這些閾值函數(shù)在全部小波空間域內(nèi)高階不可導(dǎo),擁有臨界閾值處不能平滑過渡的現(xiàn)象。因此本文提出一個(gè)帶參數(shù)的閾值函數(shù),該閾值函數(shù)擁有更高階,通過手動(dòng)調(diào)節(jié)參數(shù)使之位于硬、軟閾值函數(shù)中間,且同時(shí)擁有硬、軟閾值函數(shù)的優(yōu)點(diǎn),并在臨界閾值內(nèi)添加平滑過渡區(qū),可在閾值處理時(shí)保留一部分有用的高頻信號(hào),較好地抑制細(xì)節(jié)系數(shù)的“過扼殺”和信號(hào)振蕩現(xiàn)象。并且通過實(shí)驗(yàn)進(jìn)行仿真,仿真結(jié)果說明了本文提出的新閾值函數(shù)增大了信號(hào)的信噪比,降低了均方誤差,獲得了相對(duì)很好的去噪效果。采用帶參數(shù)閾值函數(shù)去噪過程中,針對(duì)具體的含噪信號(hào),可以靈活調(diào)節(jié)閾值函數(shù)的參數(shù),滿足不同信號(hào)處理的去噪要求。然而,在實(shí)際應(yīng)用中,待處理信號(hào)的含噪情況是不可預(yù)測(cè)或不可知的。對(duì)于這種隨機(jī)變化的含噪信號(hào)進(jìn)行去噪,閾值函數(shù)的參數(shù)不應(yīng)該也不可能是固定值。因此對(duì)于隨機(jī)含噪信號(hào)的處理,選擇適用的優(yōu)化算法來對(duì)閾值函數(shù)的參數(shù)進(jìn)行優(yōu)化,以期能夠適應(yīng)信號(hào)的變化,這也是去噪走向?qū)嵱没年P(guān)鍵。閾值函數(shù)有兩個(gè)參數(shù),函數(shù)優(yōu)化時(shí)參數(shù)較少,同時(shí)對(duì)于變化信號(hào)的處理則需在較短時(shí)間內(nèi)完成優(yōu)化目標(biāo),因此,需要收斂速率相對(duì)較高的優(yōu)化算法。通過對(duì)比模擬退火算法、遺傳算法、神經(jīng)網(wǎng)絡(luò)算法、蟻群算法等優(yōu)化算法,選取收斂速度快、精度高及易實(shí)現(xiàn)且無需過多參數(shù)調(diào)整的粒子群優(yōu)化算法。采用粒子群優(yōu)化算法,針對(duì)信號(hào)含噪情況,自動(dòng)優(yōu)化閾值函數(shù)參數(shù),實(shí)現(xiàn)去噪過程的自動(dòng)尋優(yōu)。采用基準(zhǔn)信號(hào)仿真結(jié)果表明,提出的算法可以獲得更小的均方誤差和更高的信噪比,具有去噪實(shí)用化的價(jià)值。
[Abstract]:In the computer control system, signal transmission, detection and acquisition are affected by environment and suffered different degrees of random noise pollution, regard the implementation of signal denoising is necessary. How to filter out the noise in the actual signal, and obtain the useful signal, is the current research focus. Especially high frequency and strong noise mixed signal, weak signal or non-stationary random signal, the Fu Liye transform of traditional processing non-stationary signals of these signals are not local analysis, and wavelet transform has the time-frequency analysis ability, the signal denoising effect is relatively good, its application is very extensive. Several kinds of wavelet denoising method, wavelet threshold denoising can be close to the optimal in minimum mean square error, and has a good visual effect, and is widely used and with deep research. Denoising method, wavelet threshold in wavelet decomposition, threshold The value and the threshold function is the important factor of wavelet threshold denoising. To deal with all kinds of noisy signal, wavelet basis is not the same with different characteristics, can be quite sure that is often not a wavelet function can denoising effect according to the signal of all types are optimal. At the same time, the decomposition the number, also can be determined is that the signal is not the same, not the same signal-to-noise will correspond to a decomposition denoising effect is better than or close to the best. Based on the wavelet function and decomposition level is determined to create an algorithm that can treat the signal needle to make analysis, the signal-to-noise ratio index by calculating wavelet decomposition level or different treated after the noisy signal processing improve SNR, the relation model to determine the most appropriate wavelet basis function And the decomposition level. Select the threshold function directly affects the accuracy of signal reconstruction, and for the previous hard, soft threshold function has some disadvantages: the hard threshold function is discontinuous on the threshold, this phenomenon will have discontinuous points after make denoising signal reconstruction are more likely to have additional oscillation caused by pseudo Gibbs "phenomenon, and greater than the wavelet coefficient threshold in noise disturbance usually contaminated, influence the quality of the final reconstructed signal; soft threshold function has its own drawbacks: the threshold processing, when the absolute value of wavelet coefficients greater than or equal to the threshold, the wavelet coefficients are directly taken by the threshold of this approach, the wavelet coefficients between the estimated coefficients which will cause the wavelet and the original signal has a certain deviation, will affect the final signal reconstruction greatly. According to the biography The threshold function defects, many scholars put forward the soft threshold function, the improved algorithm of hard threshold. But these intermediate threshold function in wavelet domain all high order non differentiable, with critical threshold can be a smooth transition phenomenon. Therefore this paper proposes a parameterized threshold function, the higher order has this threshold function, by manually adjusting the parameters so that at the middle of hard and soft threshold function, and also has the advantages of hard and soft threshold function, and add a smooth transition zone at a critical threshold, can keep part of the high frequency signal useful in threshold processing, restrain the detail coefficients of the "over kill" and the signal oscillation phenomenon. And through the simulation experiment, the simulation results show that the new threshold function is proposed to increase the signal-to-noise ratio, mean square error is reduced, to obtain a relatively good de-noising effect with ginseng The number of threshold function denoising process, the noisy signal is specific, can flexibly adjust the parameter of threshold function, meet the requirements of different denoising signal processing. However, in practical application, containing noise of the signal is unpredictable or unknown. For the random noise signal of denoising, threshold function parameters should not be fixed value. So for dealing with random noise signal, selection algorithm applicable to parameters of the threshold function is optimized, in order to adapt to the change of signal, which is the key to the practical denoising threshold function. There are two parameters. Function optimization and processing for signal changes less, is required to complete the optimization goal, within a short period of time, therefore, need to optimize the convergence rate is relatively high. By comparing the simulated annealing algorithm, genetic algorithm, neural Network algorithm, ant colony algorithm and other optimization algorithms, selection of fast convergence, high precision and easy realization of particle swarm optimization algorithm and without excessive parameter adjustment. Using particle swarm optimization algorithm for signal denoising, threshold function parameter optimization, realize the automatic optimization of the denoising process. The simulation results using the reference signal show that the mean square error of the proposed algorithm can get smaller and higher SNR with practical denoising value.

【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TN911.7

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