本文關(guān)鍵詞： 計算機斷層成像 壓縮感知 圖像重建 正則化參數(shù) 稀疏約束 優(yōu)化算法　出處：《中國科學院研究生院(長春光學精密機械與物理研究所)》2016年博士論文　論文類型：學位論文

【摘要】：為了減輕X射線輻射對人體和周邊環(huán)境的危害,用于醫(yī)學診斷的計算機斷層成像(Computed Tomography,CT)掃描系統(tǒng)的設(shè)計需要考慮降低輻射劑量的問題。降低采樣率,縮短掃描時間是一個直接有效的方法。然而傳統(tǒng)的圖像重建算法受到香農(nóng)柰奎斯特采樣定理的限制,其投影采樣的頻率必須達到重建目標最高頻率的兩倍以上,才能精確重建圖像,否則會導致混疊偽影的出現(xiàn),無法滿足醫(yī)學CT檢查對成像質(zhì)量的要求。近年來提出的壓縮感知(Compressed Sensing,CS)理論能夠有效提取圖像的稀疏性,從而利用其稀疏性作為先驗知識來進行斷層圖像重建,與傳統(tǒng)的濾波反投影(Filtered Back-projection,FBP)算法相比可以明顯改進重建圖像質(zhì)量。因此,結(jié)合CT掃描系統(tǒng)的特點,研究設(shè)計快速穩(wěn)定的CS算法,有效的重建CT圖像,使基于CS理論的CT系統(tǒng)圖像重建算法由理論向?qū)嶋H應(yīng)用轉(zhuǎn)化,就是本研究的意義和預(yù)期目標。目前已提出的基于CS理論的欠采樣重建算法分別以TV最小化和字典學習正則項為稀疏約束,其中基于TV最小化約束的重建算法已比較成熟。基于字典學習正則項的重建算法還存在一些待解決的問題,比如:1.正則化參數(shù)的確定。2.重建圖像中軟組織區(qū)域邊緣細節(jié)信息的保留。3.掃描數(shù)據(jù)采樣率進一步下降條件下高質(zhì)量重建圖像的問題。針對這些問題,本文提出了相應(yīng)的模型和改進方法,主要創(chuàng)新性工作包括:(1)針對字典學習重建算法中正則化參數(shù)無法有效選取的問題,建立正則化參數(shù)取值模型。正則化參數(shù)的大小與原始掃描數(shù)據(jù)的噪聲水平,掃描幾何等關(guān)系密切,該模型首先通過計算找到能夠反映當前掃描數(shù)據(jù)特點的相關(guān)參量,并通過函數(shù)擬合建立其與最佳正則化參數(shù)的函數(shù)關(guān)系。正則化參數(shù)選取模型的建立,免除了通過大量重復實驗挑選合理正則化參數(shù)的步驟,提高了重建效率,也為進一步的字典學習重建算法研究打下基礎(chǔ)。(2)為了使重建圖像能夠保留更多的軟組織邊緣細節(jié)信息,提出一種加權(quán)字典學習重建算法。基于字典學習正則項的重建算法從待重建圖像中抽取出所有大小相同且互相重疊的小圖像塊,每個小圖像塊都可以用待訓練的過完備字典稀疏表示,以此稀疏表示作為正則約束,在迭代過程中使結(jié)果圖像收斂到合理的可行解域中。加權(quán)字典學習重建算法根據(jù)每個圖像塊包含細節(jié)的多少給予不同的稀疏約束權(quán)重,更好了保留了重建圖像的細節(jié)信息。實驗結(jié)果表明,與改進前的算法相比,重建圖像歸一化平均絕對偏差更小,對于圖像中的細節(jié)部分和低對比度信息的分辨率提高,更有利于醫(yī)生的臨床診斷。(3)為了改進基于字典學習的重建算法,使其能夠適應(yīng)更低采樣率的掃描數(shù)據(jù),提出一種基于L1稀疏約束的字典學習重建算法。該算法用L1范數(shù)下的約束項代替原算法中的L2稀疏約束項,利用L1約束項更高的稀疏性適應(yīng)采樣率的進一步降低。實驗結(jié)果表明該算法在降低采樣率的條件下依然能保持較高的圖像質(zhì)量。與改進前的字典學習算法對比,L1稀疏約束項也進一步提高了同等采樣條件下圖像的空間分辨率,降低了重建圖像與真實圖像的偏差,提高了重建質(zhì)量。
[Abstract]:In order to reduce the X ray radiation on the human body and the surrounding environment, computerized tomography for medical diagnosis (Computed Tomography CT) scanning system needs to be considered in the design to reduce the radiation dose. To reduce the sampling rate, shorten the scan time is a direct and effective method. However, the traditional image reconstruction algorithm by Shannon Nai queis special sampling limit, the projection of the sampling frequency must reach the goal of reconstruction of the highest frequency of more than two times, in order to accurately reconstruct the image, otherwise it will cause aliasing artifacts, unable to meet the medical CT check on the quality of imaging requirements. Compressed sensing proposed in recent years (Compressed, Sensing, CS) theory to sparse effective extraction of the image, and use its sparsity as a prior knowledge to carry out fault image reconstruction, and the conventional filtered backprojection (Filtered Back-projection FBP) algorithm Compared with can improve the quality of image reconstruction. Therefore, combined with the characteristics of CT scanning system, CS algorithm design fast and stable, the reconstruction of CT image effectively, the CT image reconstruction algorithm based on CS theory from theory to practical application, is the significance of this study and the expected goal. The CS theory under sampling reconstruction algorithm using TV minimization and regularization for dictionary learning based on sparse constraint have been proposed, including TV reconstruction algorithm based on constrained minimization has been relatively mature. Dictionary learning regularization reconstruction algorithm has some problems to be solved, such as: 1. based on the determination of the regularization parameter preserving.3. scan data.2. reconstruction images of soft tissue regional edge information sampling rate to decline further high quality of image reconstruction conditions. To solve these problems, this paper puts forward the corresponding model and the improved method, the main To the innovative work include: (1) according to the dictionary learning regular reconstruction algorithm parameters can not be effectively selected, establishing regularization parameter model. The noise level of the regularization parameter and the size of the original scan data, scan geometry relationship, the model is first calculated to find relevant parameters of the current scan data characteristics. To reflect, and through function fitting to establish the function relationship and the optimal regularization parameter. The model of choosing the regularization parameter, from the large number of repeated experiments through selecting the reasonable regularization parameter step, improve the efficiency of the reconstruction, but also for further study to lay the foundation for the study of dictionary reconstruction algorithm. (2) in order to make the image reconstruction soft tissue can retain more edge details, we propose a weighted dictionary learning algorithm. Dictionary learning regularization reconstruction algorithm based on image reconstruction from To extract all the same size and overlapping small image blocks, each image block can be used to be trained overcomplete dictionaries for sparse, the sparse representation as regular constraints in the iterative process of the image converges to the reasonable feasible solution domain. The weighted dictionary learning algorithm according to the reconstruction of each image block contains many the details of the given sparse constraint different weights, the better retaining details of the reconstructed image. The experimental results show that compared with the former algorithm, the reconstructed image normalized mean absolute deviation is smaller, the image details and low contrast information to improve the resolution, more conducive to clinical diagnosis (3) to the doctor. The improved reconstruction algorithm based on dictionary learning, which can adapt to the lower sampling rate of scan data, proposes a learning L1 reconstruction algorithm for sparse constraint based on the dictionary. By using the method of L1 norm constraint instead of the original algorithm L2 sparse constraint, L1 constraint using higher sparsity to further reduce the sampling rate. The experimental results show that the algorithm can still maintain high image quality at lower sampling rate conditions. Compared with the improved learning algorithm of dictionary, L1 the sparsity constraints can further improve the spatial resolution of the image of the same sampling condition, reduce the reconstruction image and real image deviation, the reconstruction quality is improved.

【學位授予單位】：中國科學院研究生院(長春光學精密機械與物理研究所)
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TP391.41

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