發(fā)布時(shí)間：2018-03-04 07:10

  本文選題：壓縮感知　切入點(diǎn)：觀測(cè)矩陣　出處：《南京理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：壓縮感知理論解決了傳統(tǒng)采樣理論對(duì)帶寬要求的瓶頸,以"邊采樣邊壓縮"的方式直接對(duì)信號(hào)進(jìn)行處理,其中采樣中最關(guān)鍵的環(huán)節(jié)就是觀測(cè)矩陣的構(gòu)造。性能優(yōu)良的觀測(cè)矩陣將信號(hào)投影到低維空間,得到的觀測(cè)值包含盡可能多的原始信號(hào)的重要信息,這樣確保更精準(zhǔn)地重構(gòu)出原始信號(hào)。本文圍繞觀測(cè)矩陣的構(gòu)造問(wèn)題,深入研究了觀測(cè)矩陣的分類以及各類觀測(cè)矩陣的構(gòu)造原理和方法。針對(duì)現(xiàn)有的常用觀測(cè)矩陣存在的問(wèn)題,本文提出了相應(yīng)的構(gòu)造和改進(jìn)方法,主要的創(chuàng)新工作包括:(1)針對(duì)現(xiàn)有觀測(cè)矩陣構(gòu)造復(fù)雜且元素不是二值化的問(wèn)題,在已有的低密度奇偶觀測(cè)矩陣基礎(chǔ)上,提出一種級(jí)聯(lián)LDPC觀測(cè)矩陣的構(gòu)造方法。LDPC校驗(yàn)矩陣的構(gòu)造條件之一就是各列元素之間保持不相干性,滿足觀測(cè)矩陣的RIP準(zhǔn)則,故將其應(yīng)用于壓縮感知中作為觀測(cè)矩陣使用。級(jí)聯(lián)LDPC觀測(cè)矩陣的構(gòu)造受Mackay 1A構(gòu)造法的啟發(fā),用Gallager構(gòu)造法取代Mackay構(gòu)造法中部分內(nèi)容,由這兩者級(jí)聯(lián)生成。實(shí)驗(yàn)結(jié)果表明,級(jí)聯(lián)LDPC觀測(cè)矩陣性能優(yōu)于用單一方法構(gòu)造的LDPC觀測(cè)矩陣。(2)針對(duì)現(xiàn)有觀測(cè)矩陣存儲(chǔ)量大且不易于硬件實(shí)現(xiàn)的問(wèn)題,在LDPC觀測(cè)矩陣的基礎(chǔ)上,提出對(duì)角化LDPC觀測(cè)矩陣的構(gòu)造方法。將LDPC觀測(cè)矩陣與對(duì)角塊矩陣相結(jié)合,生成對(duì)角化LDPC觀測(cè)矩陣。對(duì)角線位置放置相同的LDPC塊,不僅簡(jiǎn)化構(gòu)造復(fù)雜度,而且能夠減小存儲(chǔ)空間,只需要存儲(chǔ)一個(gè)LDPC塊大小的元素,即可得到一個(gè)完整的對(duì)角化LDPC觀測(cè)矩陣。實(shí)驗(yàn)結(jié)果表明,對(duì)角化LDPC觀測(cè)矩陣具有以下優(yōu)勢(shì):a.構(gòu)造簡(jiǎn)單且矩陣元素少;b.重構(gòu)精度高;c.計(jì)算量和存儲(chǔ)空間小;d.方便硬件實(shí)現(xiàn)。將對(duì)角化LDPC觀測(cè)矩陣應(yīng)用于遙感圖像重構(gòu)仿真實(shí)驗(yàn),重構(gòu)效果優(yōu)于其他觀測(cè)矩陣,且重構(gòu)時(shí)間較短。(3)針對(duì)圖像數(shù)據(jù)采樣的復(fù)雜性,同時(shí)為了驗(yàn)證觀測(cè)矩陣的性能,本文設(shè)計(jì)實(shí)現(xiàn)一個(gè)壓縮感知圖像重構(gòu)仿真軟件系統(tǒng)。該軟件能夠清晰地看到壓縮感知圖像重構(gòu)的所有流程,包括圖像信號(hào)的稀疏表示、信號(hào)的感知采樣和圖像信號(hào)的重構(gòu)。軟件側(cè)重于觀測(cè)矩陣的采樣過(guò)程,可以根據(jù)需求生成所需大小的觀測(cè)矩陣,并且直觀地看到觀測(cè)矩陣的圖像,便于更形象地了解觀測(cè)矩陣。重構(gòu)后能夠看到重構(gòu)圖像以及圖像重構(gòu)的評(píng)價(jià)指標(biāo)PSNR 和 SSIM 值。
[Abstract]:Compression sensing theory solves the bottleneck of bandwidth requirement in traditional sampling theory, and directly processes the signal in the way of "edge sampling and compression". The construction of observation matrix is the most important part in sampling. The observation matrix with good performance projects the signal into low dimensional space, and the obtained observation value contains as much important information as possible of the original signal. In this paper, the classification of observation matrix and the construction principle and method of all kinds of observation matrix are studied. In this paper, the corresponding construction and improvement methods are proposed. The main innovation work includes: 1) aiming at the problem of complex construction and non-binarization of the existing observation matrix, based on the existing low density odd-even observation matrix, This paper presents a method of constructing cascaded LDPC observation matrix. One of the conditions of constructing the check matrix is that the elements of each column remain incoherent, which satisfies the RIP criterion of the observation matrix. Therefore, it is applied to compressed perception as observation matrix. The construction of cascaded LDPC observation matrix is inspired by Mackay 1A construction method, and some contents of Mackay construction method are replaced by Gallager construction method, which are generated by these two cascading methods. The experimental results show that, The performance of cascaded LDPC observation matrix is better than that of LDPC observation matrix constructed by single method. Aiming at the problem that the existing observation matrix has large storage capacity and is difficult to be implemented in hardware, the performance of cascade LDPC observation matrix is better than that of LDPC observation matrix constructed by a single method. A method of constructing diagonal LDPC observation matrix is presented. The diagonal LDPC observation matrix is generated by combining the LDPC observation matrix with diagonal block matrix. The diagonal position of the same LDPC block not only simplifies the construction complexity, but also reduces the storage space. A complete diagonal LDPC observation matrix can be obtained by simply storing an element of LDPC block size. The experimental results show that, The diagonal LDPC observation matrix has the following advantages: A. simple construction, few matrix elements, high reconstruction precision, small computation and storage space, convenient hardware realization. The diagonal LDPC observation matrix is applied to remote sensing image reconstruction simulation experiment. The reconstruction effect is better than other observation matrices, and the reconstruction time is shorter. In this paper, we design and implement a compressing perceptual image reconstruction simulation software system, which can clearly see all the processes of compressed perceptual image reconstruction, including sparse representation of image signals. The software focuses on the sampling process of the observation matrix, and can generate the observation matrix of the required size according to the requirement, and can see the image of the observation matrix intuitively. It is convenient to understand the observation matrix more vividly. After reconstruction, we can see the reconstructed image and the evaluation index PSNR and SSIM value of image reconstruction.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP391.41

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