基于稀疏與低秩的動(dòng)態(tài)核磁共振圖像重建
發(fā)布時(shí)間：2019-05-11 15:41
【摘要】：動(dòng)態(tài)核磁共振成像(Magnetic Resonance Imaging,MRI)能夠提供對(duì)運(yùn)動(dòng)器官進(jìn)行輔助診斷的圖像,因此是一門非常有用的技術(shù)并且已經(jīng)被廣泛地應(yīng)用于臨床輔助診斷。然而,MRI過程通常需要花費(fèi)很長的時(shí)間去掃描以獲得成像數(shù)據(jù),這個(gè)缺點(diǎn)限制了動(dòng)態(tài)MRI圖像可獲得的時(shí)空分辨率。為此,壓縮感知理論被引入到動(dòng)態(tài)MRI當(dāng)中去減少掃描時(shí)間,它的理論依據(jù)是:當(dāng)一個(gè)信號(hào)是稀疏或轉(zhuǎn)換稀疏時(shí),它可以從部分不完整的測試數(shù)據(jù)中完美地重構(gòu)出來。所以利用壓縮感知(Compressed Sensing,CS)理論對(duì)欠采樣的動(dòng)態(tài)MRI數(shù)據(jù)重建可以加快成像速度。近些年,低秩矩陣補(bǔ)全理論將壓縮感知理論從向量延伸到了矩陣,它能夠?qū)⒁粋�(gè)低秩矩陣的缺失或毀壞部分恢復(fù)。由于動(dòng)態(tài)磁共振圖像序列的幀與幀之間的相關(guān)性,低秩矩陣補(bǔ)全的思想可以被應(yīng)用到欠采樣的動(dòng)態(tài)MRI的重建當(dāng)中。本文的研究重點(diǎn)是如何利用壓縮感知和低秩矩陣補(bǔ)全理論對(duì)欠采樣的動(dòng)態(tài)MRI數(shù)據(jù)進(jìn)行重建,主要工作如下:首先,我們提出了一種將局部和全局低秩性相結(jié)合的動(dòng)態(tài)MRI重建算法。由于動(dòng)態(tài)MRI的空間和時(shí)間維都存在很大的相關(guān)性,若這些相關(guān)性能夠在圖像重建的過程中被有效地利用,則能夠提高重建圖像的時(shí)空分辨率。本文中,我們通過將3D動(dòng)態(tài)MRI圖像序列的每一幀向量化之后獲得一個(gè)2D矩陣,然后再從這個(gè)2D矩陣中提取重疊的塊。對(duì)于每一個(gè)提取的塊,我們在一個(gè)局部的窗內(nèi)尋找一定數(shù)量的相似塊并由它們組成一個(gè)低秩矩陣,然后再使用一個(gè)非凸函數(shù)來估計(jì)這些低秩矩陣。至此,我們充分利用了時(shí)間維的局部相關(guān)性,為了獲得更好的圖像質(zhì)量,我們使用了核范數(shù)對(duì)時(shí)間維的全局相關(guān)性進(jìn)行了低秩懲罰。最后通過和一些最先進(jìn)的方法進(jìn)行對(duì)比,驗(yàn)證了我們提出的算法的高效性。然后,我們又提出了一種基于低秩約束和3D稀疏轉(zhuǎn)換的將圖像背景和前景分離的動(dòng)態(tài)MRI重建算法。由于動(dòng)態(tài)MRI和視頻序列的相似性,所以它可以被看成是背景元素和動(dòng)態(tài)元素的結(jié)合,因此我們基于魯棒的主成分分析(Robust PrincipalComponent Analysis,RPCA)思想將它分解成了背景和動(dòng)態(tài)元素兩部分,再分別進(jìn)行重建。對(duì)于背景部分,我們利用了一個(gè)基于塊的非凸約束去對(duì)它進(jìn)行低秩約束;而動(dòng)態(tài)元素部分,我們則是采用了一個(gè)3D稀疏轉(zhuǎn)換對(duì)它進(jìn)行稀疏約束。然后我們使用了變量分離和交替優(yōu)化算法對(duì)提出的優(yōu)化問題進(jìn)行了求解,可以分別得到背景部分和前景部分的解,只要將兩者相加就可以獲得最終的重建圖像。實(shí)驗(yàn)結(jié)果表明,提出的這個(gè)算法可以恢復(fù)出更清晰的圖像,并且圖像的細(xì)節(jié)也保存得更好。
[Abstract]:Dynamic nuclear magnetic resonance imaging (Magnetic Resonance Imaging,MRI) can provide images of auxiliary diagnosis of motor organs, so it is a very useful technique and has been widely used in clinical auxiliary diagnosis. However, the MRI process usually takes a long time to scan to obtain imaging data, which limits the temporal and spatial resolution available to dynamic MRI images. Therefore, compression perception theory is introduced into dynamic MRI to reduce scanning time. Its theoretical basis is that when a signal is sparse or transformed sparse, it can be perfectly reconstructed from some incomplete test data. Therefore, compressed sensing (Compressed Sensing,CS) theory can be used to reconstruct undersampled dynamic MRI data to speed up the imaging speed. In recent years, the low rank matrix completion theory extends the compressed perception theory from vector to matrix, which can restore the missing or destroyed part of a low rank matrix. Because of the correlation between frames and frames in dynamic magnetic resonance image sequences, the idea of low rank matrix completion can be applied to the reconstruction of undersampled dynamic MRI. The focus of this paper is how to reconstruct the undersampled dynamic MRI data by using compressed perception and low rank matrix completion theory. The main work is as follows: first, We propose a dynamic MRI reconstruction algorithm which combines local and global low rank. Because there is a great correlation between the spatial and temporal dimensions of dynamic MRI, if these correlation can be effectively used in the process of image reconstruction, the spatial and temporal resolution of the reconstructed image can be improved. In this paper, we obtain a 2D matrix by vector each frame of 3D dynamic MRI image sequence, and then extract overlapping blocks from the 2D matrix. For each extracted block, we look for a certain number of similar blocks in a local window and form a low rank matrix from them, and then use a nonconvex function to estimate these low rank matrices. So far, we make full use of the local correlation of time dimension. In order to obtain better image quality, we use kernel norm to punish the global correlation of time dimension with low rank. Finally, the efficiency of the proposed algorithm is verified by comparing with some of the most advanced methods. Then, we propose a dynamic MRI reconstruction algorithm based on low rank constraint and 3D sparse transformation to separate the background and foreground of the image. Because of the similarity between dynamic MRI and video sequence, it can be regarded as the combination of background element and dynamic element, so we decompose it into two parts based on robust principal component analysis (Robust PrincipalComponent Analysis,RPCA). Then the reconstruction was carried out separately. For the background part, we use a block-based nonconvex constraint to constrain it with low rank, while in the dynamic element part, we use a 3D sparse transformation to sparse it. Then we use variable separation and alternating optimization algorithm to solve the proposed optimization problem, and we can get the solution of the background part and the foreground part respectively, and the final reconstruction image can be obtained by adding the two algorithms. The experimental results show that the proposed algorithm can restore clearer images and save the details of the images better.
【學(xué)位授予單位】：中國科學(xué)技術(shù)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
本文編號(hào)：2474621
[Abstract]:Dynamic nuclear magnetic resonance imaging (Magnetic Resonance Imaging,MRI) can provide images of auxiliary diagnosis of motor organs, so it is a very useful technique and has been widely used in clinical auxiliary diagnosis. However, the MRI process usually takes a long time to scan to obtain imaging data, which limits the temporal and spatial resolution available to dynamic MRI images. Therefore, compression perception theory is introduced into dynamic MRI to reduce scanning time. Its theoretical basis is that when a signal is sparse or transformed sparse, it can be perfectly reconstructed from some incomplete test data. Therefore, compressed sensing (Compressed Sensing,CS) theory can be used to reconstruct undersampled dynamic MRI data to speed up the imaging speed. In recent years, the low rank matrix completion theory extends the compressed perception theory from vector to matrix, which can restore the missing or destroyed part of a low rank matrix. Because of the correlation between frames and frames in dynamic magnetic resonance image sequences, the idea of low rank matrix completion can be applied to the reconstruction of undersampled dynamic MRI. The focus of this paper is how to reconstruct the undersampled dynamic MRI data by using compressed perception and low rank matrix completion theory. The main work is as follows: first, We propose a dynamic MRI reconstruction algorithm which combines local and global low rank. Because there is a great correlation between the spatial and temporal dimensions of dynamic MRI, if these correlation can be effectively used in the process of image reconstruction, the spatial and temporal resolution of the reconstructed image can be improved. In this paper, we obtain a 2D matrix by vector each frame of 3D dynamic MRI image sequence, and then extract overlapping blocks from the 2D matrix. For each extracted block, we look for a certain number of similar blocks in a local window and form a low rank matrix from them, and then use a nonconvex function to estimate these low rank matrices. So far, we make full use of the local correlation of time dimension. In order to obtain better image quality, we use kernel norm to punish the global correlation of time dimension with low rank. Finally, the efficiency of the proposed algorithm is verified by comparing with some of the most advanced methods. Then, we propose a dynamic MRI reconstruction algorithm based on low rank constraint and 3D sparse transformation to separate the background and foreground of the image. Because of the similarity between dynamic MRI and video sequence, it can be regarded as the combination of background element and dynamic element, so we decompose it into two parts based on robust principal component analysis (Robust PrincipalComponent Analysis,RPCA). Then the reconstruction was carried out separately. For the background part, we use a block-based nonconvex constraint to constrain it with low rank, while in the dynamic element part, we use a 3D sparse transformation to sparse it. Then we use variable separation and alternating optimization algorithm to solve the proposed optimization problem, and we can get the solution of the background part and the foreground part respectively, and the final reconstruction image can be obtained by adding the two algorithms. The experimental results show that the proposed algorithm can restore clearer images and save the details of the images better.
【學(xué)位授予單位】：中國科學(xué)技術(shù)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
【參考文獻(xiàn)】
相關(guān)期刊論文 前2條
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