【摘要】：眾所周知，在人們的日常生活中數(shù)字圖像隨處可見，諸如遙感成像、安全監(jiān)控、醫(yī)學成像等。隨著對數(shù)字圖像的需求越來越多，隨之而來的對數(shù)字圖像質(zhì)量的要求也越來越高，能夠體現(xiàn)更多細節(jié)信息的高分辨率圖像成為圖像重構技術中研究的核心內(nèi)容。圖像超分辨率重構技術就是利用同一場景不同環(huán)境下獲得的多幅低分辨率圖像來重構一幅高分辨率圖像。由于成像設備、光照、拍攝物與成像設備間的相對位移等因素的干擾，獲取的圖像分辨率往往都比較低。但這些由于不同因素發(fā)生降質(zhì)的圖像中包含了更豐富的圖像信息，將這些信息融合到一幅圖像中，再經(jīng)過圖像重構技術對其進行恢復，所獲得的圖像具有更高的分辨率。圖像超分辨率重構技術成為獲取高分辨率圖像的關鍵技術之一。 壓縮感知理論作為一個新的采樣理論，它可以在遠小于奈奎斯特采樣率的條件下獲取信號的離散樣本，保證信號的無失真重構。該理論在現(xiàn)代信號處理領域有著廣闊的發(fā)展空間和實用性。本文的主要工作內(nèi)容為以下幾項： 第一、對圖像超分辨率技術的研究現(xiàn)狀進行了簡單的介紹，并針對該技術的數(shù)學特性進行了詳細地分析。概述了該技術的三項核心研究內(nèi)容：圖像配準、圖像融合及圖像重構，歸納總結了幾種圖像質(zhì)量評價標準。 第二、針對不同的應用范圍，首先對圖像配準技術進行了分類總結，其中針對基于特征的SIFT圖像配準進行了詳細的數(shù)學算法分析，并進行了仿真實驗，驗證了其旋轉尺度不變性及模糊不變性。對于拉普拉斯金字塔圖像融合技術進行了整理與分析，并進行了仿真實驗。 第三、對圖像超分辨率重構算法進行了分類介紹，總結了各類算法的優(yōu)缺點。對其中空域法中的非均勻樣本內(nèi)插法、迭代反向投影法、最大后驗概率估計法和凸集投影法進行了詳細的數(shù)學分析，對比分析了優(yōu)缺點。并針對凸集投影法提出了一種優(yōu)化算法，該算法首先將圖像進行區(qū)域劃分插值，然后利用二維非線性濾波加強圖像邊緣，仿真實驗驗證了優(yōu)化算法的重構圖像含有更多的細節(jié)信息。 第四、已有的研究證明，圖像在小波域具有高度可壓縮的性質(zhì)，可以利用壓縮感知理論對單幅圖像進行精確地超分辨率重構。重構算法需要將低通濾波器加入到測量矩陣里使得圖像超分辨率重構問題能夠滿足壓縮感知理論的約束有限等距性質(zhì)。針對正交匹配追蹤重構算法進行了分析及優(yōu)化，，優(yōu)化算法采用每次選取稀疏度K個原子來更新支撐集，并采用二分坐標下降迭代法加快收斂速度，仿真實驗驗證了優(yōu)化算法在重構質(zhì)量和重構時間上的優(yōu)越性。
[Abstract]:It is well known that digital images can be seen everywhere in people's daily life, such as remote sensing imaging, security monitoring, medical imaging and so on. With the increasing demand for digital image, the quality of digital image becomes higher and higher. High-resolution image, which can reflect more detail information, has become the core of image reconstruction technology. Image super-resolution reconstruction technique is to reconstruct a high-resolution image by using multiple low-resolution images obtained in different environments of the same scene. Because of the interference of imaging equipment, illumination, relative displacement between camera and imaging equipment, the resolution of the obtained image is usually low. However, these images, which are degraded by different factors, contain more abundant image information. They are fused into a single image, and then restored by image reconstruction technology. The obtained images have higher resolution. Super-resolution reconstruction has become one of the key technologies for obtaining high-resolution images. As a new sampling theory, compressed sensing theory can obtain discrete samples of signals far less than Nyquist sampling rate, and guarantee signal reconstruction without distortion. The theory has wide development space and practicability in the field of modern signal processing. The main contents of this paper are as follows: firstly, the research status of image super-resolution technology is briefly introduced, and the mathematical characteristics of this technology are analyzed in detail. This paper summarizes three core research contents of this technology: image registration, image fusion and image reconstruction, and summarizes several evaluation criteria of image quality. Secondly, aiming at the different application areas, the image registration technology is classified and summarized firstly, among which, the mathematical algorithm analysis of feature-based SIFT image registration is carried out in detail, and the simulation experiment is carried out. The rotation scale invariance and fuzzy invariance are verified. The image fusion technology of Laplacian pyramid is sorted and analyzed, and the simulation experiment is carried out. Thirdly, the classification of image super-resolution reconstruction algorithm is introduced, and the advantages and disadvantages of all kinds of algorithms are summarized. In this paper, the non-uniform sample interpolation method, iterative back projection method, maximum posterior probability estimation method and convex set projection method are analyzed in detail, and their advantages and disadvantages are compared and analyzed. An optimization algorithm for convex set projection method is proposed. Firstly, the image is divided into regions and interpolated, and then two-dimensional nonlinear filtering is used to enhance the edge of the image. Simulation results show that the reconstructed image contains more detailed information. Fourth, it has been proved that the image is highly compressible in wavelet domain, and the compression sensing theory can be used to reconstruct the super-resolution of a single image accurately. The reconstruction algorithm needs to add the low-pass filter to the measurement matrix so that the super-resolution reconstruction of the image can satisfy the constrained finite isometric property of the compression sensing theory. The orthogonal matching tracking reconstruction algorithm is analyzed and optimized. In the optimization algorithm, K atoms are selected each time to update the support set, and the binary coordinate descent iteration method is used to accelerate the convergence speed. Simulation results show the superiority of the optimization algorithm in reconstruction quality and reconstruction time.
【學位授予單位】：吉林大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.73

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