本文關(guān)鍵詞： 圖像去噪 高階消失矩 二進(jìn)小波濾波器 閾值函數(shù)　出處：《新疆師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：現(xiàn)實(shí)生活中,噪聲的存在依舊是無(wú)法忽視的問題。近些年來(lái),隨著科技的不斷發(fā)展,及小波理論的進(jìn)一步的填充,小波在圖像去噪中變得越來(lái)越有優(yōu)勢(shì),其已逐步成為圖像處理的重要研究?jī)?nèi)容之一。小波變換領(lǐng)域中正交小波研究居多,但是其下采樣,使得圖像變換到小波域后會(huì)造成圖像位置信息發(fā)生偏差,從而引起視覺上的變形。故文章構(gòu)造出具有高階消失矩的二進(jìn)小波濾波器和卷積型正交小波,還提出一種新的閾值函數(shù)同時(shí)作用對(duì)圖像進(jìn)行去噪處理,并將去噪后的圖象的PSNR數(shù)據(jù)和效果進(jìn)行比較與分析。最終由仿真實(shí)驗(yàn)得出,基于二進(jìn)小波的閾值去噪方法是一種有效的圖像去噪方法。主要研究?jī)?nèi)容如下:(1)介紹本課題的研究背景和意義,并將小波閾值去噪的發(fā)展和現(xiàn)狀、文章的結(jié)構(gòu)與安排、文章的創(chuàng)新點(diǎn)進(jìn)行簡(jiǎn)述。(2)小波變換的基本的理論,簡(jiǎn)單的敘述連續(xù)、離散小波變換的定義和相關(guān)的定理、重點(diǎn)去介紹與二進(jìn)小波相關(guān)的一些理論,最后將詳細(xì)介紹Mallat算法和a?trous算法這兩種快速算法,在一定程度上突出這兩種算法的差異。(3)在深入分析軟、硬閾值函數(shù)的優(yōu)缺點(diǎn)的基礎(chǔ)上,引入改進(jìn)的閾值函數(shù),并構(gòu)造出卷積型正交小波對(duì)圖像進(jìn)行去噪分析;(4)正交小波變換不具有平移不變性,使得去噪后的圖像容易出現(xiàn)Gibbs現(xiàn)象而不能滿足人類視覺要求。為了抑制這種現(xiàn)象,引入了具有平移不變性的二進(jìn)小波變換,構(gòu)造具有高階消失矩的二進(jìn)小波濾波器結(jié)合改進(jìn)的閾值函數(shù),提出基于二進(jìn)小波變換的閾值去噪方法。仿真實(shí)驗(yàn)結(jié)果表明,該方法無(wú)論在峰值信噪比方面還是在視覺效果方面與小波硬閾值、軟閾值去噪方法相比都有明顯的提高和改善,是一種有效的圖像去噪方法。
[Abstract]:In real life, the existence of noise is still a problem that can not be ignored. In recent years, with the development of science and technology and the further filling of wavelet theory, wavelet has become more and more advantageous in image denoising. It has gradually become one of the important research contents of image processing. In the field of wavelet transform, the research on orthogonal wavelet is more and more, but its down-sampling results in the deviation of image position information when the image is transformed into wavelet domain. Therefore, a dyadic wavelet filter with high order vanishing moments and convolutional orthogonal wavelet are constructed, and a new threshold function is proposed to de-noise the image simultaneously. The PSNR data and effect of the denoised image are compared and analyzed. The threshold denoising method based on binary wavelet is an effective image denoising method. The main research contents are as follows: 1) introduce the research background and significance of this subject, and introduce the development and present situation of wavelet threshold denoising, the structure and arrangement of this paper. The innovation of this paper is to introduce the basic theory of wavelet transform, simply describe the definition of continuous wavelet transform, discrete wavelet transform and related theorems, focus on introducing some theories related to dyadic wavelet, and finally introduce Mallat algorithm and a? On the basis of analyzing the advantages and disadvantages of the soft and hard threshold functions, the improved threshold function is introduced. A convolutional orthogonal wavelet is constructed for denoising the image. (4) the orthogonal wavelet transform has no translation invariance, which makes the denoised image prone to Gibbs phenomenon and unable to meet the human visual requirements. In this paper, a binary wavelet transform with translational invariance is introduced to construct a dyadic wavelet filter with high order vanishing moments combined with an improved threshold function. A threshold denoising method based on dyadic wavelet transform is proposed. The simulation results show that, Compared with wavelet hard threshold and soft threshold denoising method, this method is an effective image denoising method, both in the aspect of peak signal-to-noise ratio (PSNR) and visual effect.
【學(xué)位授予單位】：新疆師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP391.41

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