本文選題：Grouplet變換 + 壓縮感知��； 參考：《南昌航空大學(xué)》2017年碩士論文

【摘要】：本論文在國(guó)家自然科學(xué)基金(51261024,51675258)、國(guó)家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2016YFF0203000)、江西省教育廳科學(xué)技術(shù)研究項(xiàng)目(GJJ150699)和廣東省數(shù)字信號(hào)與圖像處理技術(shù)重點(diǎn)實(shí)驗(yàn)室開(kāi)放課題(2014GDDSIPL-01)共同資助下,圍繞Grouplet變換為中心,針對(duì)圖像重構(gòu)、圖像去噪、圖像融合方面展開(kāi)研究,結(jié)合新的壓縮采樣理論,提出一系列新的算法,并取得了一些創(chuàng)新性的成果。本文的主要內(nèi)容包括以下幾方面:第一章,詳細(xì)論述了結(jié)合Grouplet變換與壓縮感知的必要性、本課題的提出及其研究意義,系統(tǒng)介紹了超小波的發(fā)展及研究進(jìn)展,尤其是Grouplet變換的國(guó)內(nèi)外研究現(xiàn)狀,最后給出了本文的主要內(nèi)容和創(chuàng)新之處。第二章,結(jié)合Grouplet變換與壓縮感知算法各自的優(yōu)點(diǎn),提出了基于Grouplet-壓縮感知(Grouplet-CS)的圖像重構(gòu)方法。該方法的特色在于充分將Grouplet變換稀疏表示融合于壓縮感知中,既最大限度的利用圖像的幾何特征,又消除了傳統(tǒng)奈奎斯特采樣理論造成的冗余與資源的浪費(fèi),可以進(jìn)一步挖掘圖像的方向、尺度等的紋理信息,使得即使很少的采樣點(diǎn)數(shù)也可恢復(fù)出較清晰的圖像質(zhì)量。通過(guò)對(duì)Lena仿真與SAR圖像的重構(gòu)中,與小波變換壓縮感知方法進(jìn)行對(duì)比分析,證明了該方法一方面降低了傳統(tǒng)方法的稀疏度和采樣率,另一方面還提高了圖像的重構(gòu)質(zhì)量。另外,還對(duì)不同的重構(gòu)方法進(jìn)行了對(duì)比,研究表明在相同的Grouplet稀疏表示和相同的壓縮比下,ROMP算法整體優(yōu)于OMP算法。第三章,引入貝葉斯壓縮感知的思想,在傳統(tǒng)貝葉斯變分算法的基礎(chǔ)上經(jīng)過(guò)改進(jìn),提出了適合二維的新的變分貝葉斯壓縮感知重構(gòu)算法,并結(jié)合Grouplet變換在稀疏表示方面的優(yōu)勢(shì),提出了Grouplet-貝葉斯壓縮感知(Grouplet-BCS)算法。提出的算法主要針對(duì)實(shí)際中圖像會(huì)夾雜有噪聲的情況,針對(duì)是否含噪以及含噪強(qiáng)度的大小選擇Grouplet-BCS算法來(lái)自適應(yīng)地降噪。經(jīng)過(guò)Lena仿真研究,以及將其用于SAR圖像的消噪中,并且與Grouplet-CS算法作比較,證明了提出的算法不僅降低了噪聲對(duì)圖像的污染,而且也在重構(gòu)精確度方面有顯著提高。第四章,論述了小波閾值消噪的特點(diǎn)以及存在的缺陷,針對(duì)小波閾值消噪中存在的問(wèn)題,提出自適應(yīng)Grouplet閾值消噪,并詳細(xì)論證了其消噪原理和算法過(guò)程。在此基礎(chǔ)上,提出了自適應(yīng)Grouplet-CS算法和自適應(yīng)Grouplet-BCS算法,并將其用于圖像消噪中。通過(guò)仿真實(shí)驗(yàn),將幾類(lèi)算法與傳統(tǒng)的小波閾值消噪方法作對(duì)比,以及將其用于SAR圖像中,分析各種方法的適用性。第五章,利用Grouplet變換可以消除圖像的大冗余,在圖像的各尺度方向、紋理上的深度挖掘的優(yōu)勢(shì),結(jié)合脈沖耦合神經(jīng)網(wǎng)絡(luò)(PCNN)可以從復(fù)雜背景下獲得有利信息的特點(diǎn),提出了Grouplet-PCNN融合算法。通過(guò)與PCNN、NSCT-PCNN以及小波-PCNN做仿真對(duì)比,證明了經(jīng)過(guò)Grouplet-PCNN融合算法得到的融合圖像信息是最豐富全面的,像素也是最高的,各紋理、邊緣等細(xì)節(jié)特征也是最明顯的。最后通過(guò)對(duì)斷口圖像的工程應(yīng)用,使得上述結(jié)論得到了有效驗(yàn)證。第六章,對(duì)各個(gè)章節(jié)作出總結(jié),并指出仍需改進(jìn)優(yōu)化的地方及可以繼續(xù)研究深入的發(fā)展方向。
[Abstract]:This paper is based on the National Natural Science Foundation (5126102451675258), the national key research and development project (2016YFF0203000), the science and technology research project of the Jiangxi Provincial Education Department (GJJ150699) and the open subject (2014GDDSIPL-01) of the Key Laboratory of digital signal and image processing technology in Guangdong. Such as reconstruction, image denoising, image fusion, combined with the new compression sampling theory, a series of new algorithms are proposed and some innovative achievements have been obtained. The main contents of this paper include the following aspects: Chapter 1, the necessity of combining Grouplet transform and compression perception is discussed in detail, and the proposal and research meaning of this subject are presented. It systematically introduces the development and research progress of super wavelet, especially the research status of Grouplet transform at home and abroad. Finally, it gives the main content and innovation in this paper. In the second chapter, combining the advantages of Grouplet transform and compressed sensing algorithm, a method of image reconstruction based on Grouplet- compression perception (Grouplet-CS) is proposed. The feature of the method is that the sparse representation of Grouplet transform is fully integrated into the compressed sensing, which not only makes the maximum use of the geometric features of the image, but also eliminates the redundancy and the waste of resources caused by the traditional Nyquist sampling theory, and can further excavate the texture information of the direction and scale of the image, making even a few sampling points. Compared with the wavelet transform compression sensing method in the reconstruction of Lena simulation and SAR image, it is proved that the method reduces the sparsity and sampling rate of the traditional method on the one hand, and also improves the quality of the reconstructed image on the other hand. In addition, the different reconstruction methods are also carried out. The research shows that under the same Grouplet sparse representation and the same compression ratio, the ROMP algorithm is better than the OMP algorithm. In the third chapter, the idea of Bias compression perception is introduced. On the basis of the traditional Bias variational algorithm, a new variational Bias compression perception reconstruction algorithm is proposed, which combines with the Grouplet. For the advantage of sparse representation, Grouplet- Bayesian compression perception (Grouplet-BCS) algorithm is proposed. The proposed algorithm is mainly aimed at the situation of noise in the actual image. The Grouplet-BCS algorithm is selected from adaptive noise reduction in view of whether the noise and the noise intensity of the algorithm come from the adaptive noise reduction. After the Lena simulation study, and the application of it to SAR In the image denoising, and compared with the Grouplet-CS algorithm, it is proved that the proposed algorithm not only reduces the noise pollution to the image, but also has a significant improvement in the reconstruction accuracy. Fourth chapter, the characteristics of the wavelet threshold denoising and the existing defects are discussed, and the adaptive Group is proposed for the problem of the small wave threshold de-noising. Let threshold de-noising, and demonstrates its denoising principle and algorithm process in detail. On this basis, the adaptive Grouplet-CS algorithm and adaptive Grouplet-BCS algorithm are proposed and used in image denoising. Through simulation experiments, several kinds of algorithms are compared with traditional wavelet threshold denoising method, and they are used in SAR images to analyze each other. In the fifth chapter, the fifth chapter, using the Grouplet transform to eliminate the large redundancy of the image, the advantage of the depth mining in the direction of the image and the depth of the texture, combined with the pulse coupled neural network (PCNN) can obtain the favorable information from the complex background, and put forward the Grouplet-PCNN fusion algorithm, through PCNN, NSCT-PCNN and The simulation and comparison of the wavelet -PCNN show that the fusion image information obtained through the Grouplet-PCNN fusion algorithm is the most abundant, the pixel is the highest, and the details of the texture and edge are most obvious. Finally, the conclusion is effectively verified by the engineering application of the fractured image. The sixth chapter is made to each chapter. Summarize and point out the areas that need to be improved and further research directions.

【學(xué)位授予單位】：南昌航空大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP391.41

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