本文關鍵詞： 超分辨率 低秩 稀疏 非局部相似性 l_(1/2)正則 迭代反投影　出處：《華東師范大學》2017年碩士論文　論文類型：學位論文

【摘要】：作為計算機視覺領域中的經(jīng)典問題,圖像超分辨率重建旨在通過一幅或者多幅低分辨率圖像,恢復對應的較高分辨率的圖像。但是,給定一幅低分辨率的輸入圖像,超分辨問題存在多重解,因而我們需要借助一些合適的先驗知識來克服上述難題。目前,研究者提出的許多算法都可以取得不錯的效果,但這些算法的結果可能會受到異常值的影響,產(chǎn)生一些不屬于原始圖像的額外細節(jié)。在本文中,針對圖像超分辨率問題,我們主要闡述以下兩大解決方案:(a)基于非局部稀疏和低秩正則的單幅圖像超分辨重建算法。其主要通過非局部冗余性來恢復圖像的潛在特征。在該算法中,我們對每個圖像塊提取相似局部結構,然后向量化形成矩陣。借助于將上述矩陣分解成低秩和稀疏兩部分,來有效地正則圖像超分辨率重建問題的不適定性。在沒有異常值以及圖像塊差異的情況下,可以利用低秩矩陣來近似相似圖像塊矩陣。然而,相似圖像塊之間必定存在細微不同,而且在重建過程中可能會受到異常值的干擾,因此我們將上述矩陣分解成了低秩成份和稀疏成份兩部分。我們再結合與低分辨率圖像逼近的保真項,最終形成了超分辨模型。(b)基于l_(1/2)和非局部低秩稀疏正則的圖像超分辨重建算法。鑒于l1/2范數(shù)約束所獲得的解比l1范數(shù)更稀疏的特性,本算法以稀疏表達算法為基礎,運用l1/2范數(shù)正則表達系數(shù)的稀疏性,結合圖像塊對字典聯(lián)合訓練,獲得了包含豐富細節(jié)內容的圖像重建初始值。為了進一步提高圖像重建質量,我們以非局部稀疏和低秩正則項作為約束,運用迭代反投影思想,把初始恢復值反投影到退化圖像的解空間中。在重建更多細節(jié)的同時,較好地保留了輸入圖像的結構特征。大量測試數(shù)據(jù)顯示,所提出的算法獲得了具有競爭性的超分辨率結果,能夠重建出更多的圖像細節(jié),擁有較清晰的圖像邊緣信息,同時有效地抑制了偽影以及異常值。
[Abstract]:As a classical problem in the field of computer vision, image super-resolution reconstruction aims to restore the corresponding high-resolution image through one or more low-resolution images. Given a low-resolution input image, the super-resolution problem has multiple solutions, so we need to use some appropriate prior knowledge to overcome the above problem. Many of the algorithms proposed by the researchers can achieve good results, but the results of these algorithms may be affected by the outliers, resulting in some additional details that do not belong to the original image. Aiming at the problem of image super-resolution. Let's focus on the following two major solutions:. The super-resolution reconstruction algorithm based on non-local sparse and low-rank regularization is mainly used to restore the potential features of the image by non-local redundancy. We extract similar local structures for each image block, then vectorize to form a matrix, which is decomposed into two parts, low rank and sparse. In the case of no outliers and block differences, the low rank matrix can be used to approximate the similar image block matrix. There must be subtle differences between similar image blocks and may be disturbed by outliers during reconstruction. So we decompose the matrix into two parts: low rank component and sparse component. We combine the fidelity term with the approximation of low resolution image. The superresolution model. And non-local low-rank sparse canonical image super-resolution reconstruction algorithm. The solution obtained by L _ 1 / 2 norm constraint is more sparse than l _ 1 norm. Based on sparse representation algorithm, this algorithm uses the sparsity of L / 2 norm canonical expression coefficients and combines image blocks to train dictionaries. In order to further improve the image reconstruction quality, we use the non-local sparse and low-rank regular terms as constraints, and use the iterative back-projection idea. The initial restoration value is projected back into the solution space of the degraded image. While more details are reconstructed, the structural features of the input image are well preserved. A large number of test data are shown. The proposed algorithm can obtain competitive super-resolution results, can reconstruct more image details, have clear image edge information, and effectively suppress artifacts and outliers.
【學位授予單位】：華東師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP391.41

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