【摘要】：磁共振成像(MRI)技術(shù)是一種可以對(duì)活體器官和組織做出詳細(xì)的器官和組織圖像的醫(yī)療成像手段,其優(yōu)勢(shì)是對(duì)人體無(wú)損傷、無(wú)輻射等傷害。但是MRI的不足是成像速度慢,目前有兩種方法可以解決這個(gè)不足,方法一是采用對(duì)硬件進(jìn)行改進(jìn),例如利用多線圈進(jìn)行成像、設(shè)計(jì)快速階梯矩陣序列等;方法二通過(guò)減少K空間數(shù)據(jù)的采集量,再利用重建算法進(jìn)行圖像重建,此方法又稱K空間重建。其中部分K空間重建不需要對(duì)硬件進(jìn)行改進(jìn),只需要對(duì)K空間重建算法改進(jìn)即可達(dá)到提高成像速度的目的。由于稀疏表示和壓縮感知理論的發(fā)展為通過(guò)對(duì)K空間的數(shù)據(jù)有效的重建MRI圖像提供了強(qiáng)有力的理論基礎(chǔ),由部分K空間數(shù)據(jù)重建MRI圖像本質(zhì)上是一種對(duì)反問(wèn)題求解,即通過(guò)少量的K空間數(shù)據(jù)求出完整的K空間數(shù)據(jù)的過(guò)程,而反問(wèn)題求解的關(guān)鍵是利用有效先驗(yàn)信息。本文主要研究圖像中的先驗(yàn)信息,再結(jié)合快速的重建算法進(jìn)行重建,并且設(shè)計(jì)了有效的循環(huán)測(cè)量矩陣,主要內(nèi)容如下:(1)壓縮感知磁共振成像測(cè)量矩陣的設(shè)計(jì)需要滿足與稀疏變換矩陣的非相干性,同時(shí)還要保證能夠應(yīng)用到硬件。本文從循環(huán)測(cè)量矩陣生成元素的相位和幅值兩個(gè)方面研究?jī)?yōu)化并構(gòu)造了循環(huán)測(cè)量矩陣,提出了交替循環(huán)尋優(yōu)方式生成元素的幅值再結(jié)合混沌的隨機(jī)相位,以此來(lái)實(shí)現(xiàn)循環(huán)測(cè)量矩陣的優(yōu)化。再和現(xiàn)有的循環(huán)矩陣進(jìn)行比較,本文構(gòu)造的循環(huán)測(cè)量矩陣對(duì)應(yīng)的等價(jià)字典列向量之間的互相干性更低,在測(cè)量數(shù)據(jù)相同的情況下,重建圖像的質(zhì)量更好。(2)曲波分析是一種方向性多尺度的分析方法,它是在小波分析和脊波分析的基礎(chǔ)上發(fā)展而來(lái)的。構(gòu)建的曲波變換能夠強(qiáng)化圖像的邊緣以及解決圖像跳躍性奇異點(diǎn)的問(wèn)題。交替方向乘子算法(Alternating Direction Method of Multipliers,簡(jiǎn)稱ADMM)可有效的解決可分離凸規(guī)劃問(wèn)題,通過(guò)對(duì)目標(biāo)函數(shù)的1l范數(shù)進(jìn)行迭代,從而降低算法的計(jì)算復(fù)雜度,加快了算法的收斂時(shí)間。本文在交替乘子算法的基礎(chǔ)上,利用曲波變換、全變差作為正則項(xiàng),對(duì)壓縮感知磁共振圖像進(jìn)行重建。此方法能夠充分挖掘磁共振圖像在不同變換域中的不同特征的稀疏性,在測(cè)量矩陣相同的基礎(chǔ)上,重建質(zhì)量得到了提升。
[Abstract]:Magnetic resonance imaging (MRI) is a kind of medical imaging method which can make detailed organ and tissue images of living organs and tissues. Its advantage is that it has no harm to human body and radiation. However, the disadvantage of MRI is that the imaging speed is slow. There are two methods to solve this problem. The first method is to improve the hardware, such as using multi-coil imaging, designing the fast step matrix sequence and so on. Second, by reducing the amount of K spatial data acquisition, and then using the reconstruction algorithm for image reconstruction, this method is also called K space reconstruction. Some of the K-space reconstruction do not need to improve the hardware, only need to improve the K-space reconstruction algorithm to achieve the purpose of improving the imaging speed. As the development of sparse representation and compressed perception theory provides a strong theoretical basis for the efficient reconstruction of MRI images from K-space data, the reconstruction of MRI images from partial K-space data is essentially a kind of inverse problem solving. That is to say, the process of finding complete K spatial data through a small amount of K spatial data, and the key to solve inverse problem is to use effective prior information. This paper mainly studies the priori information in the image, and then combines the fast reconstruction algorithm to reconstruct the image, and designs an effective cycle measurement matrix. The main contents are as follows: (1) the design of the compressed perceptual magnetic resonance imaging measurement matrix needs to satisfy the non-coherence with the sparse transformation matrix and ensure that it can be applied to the hardware at the same time. In this paper, the phase and amplitude of the elements generated by the cyclic measurement matrix are studied and optimized, and the cyclic measurement matrix is constructed. The alternating cycle optimization method is proposed to generate the amplitudes of the elements combined with the random phase of chaos. In this way, the circulatory measurement matrix is optimized. Compared with the existing cyclic matrix, the corresponding equivalent dictionary column vector of the circular measurement matrix constructed in this paper has lower coherence, and the same measurement data is obtained. The quality of reconstructed image is better. (2) Qu Bo analysis is a directional multi-scale analysis method which is developed on the basis of wavelet analysis and ridgelet analysis. The constructed Qu Bo transform can enhance the edge of the image and solve the problem of jumping singularity. The alternating direction multiplier algorithm (Alternating Direction Method of Multipliers,) can effectively solve the separable convex programming problem. By iterating the 1l norm of the objective function, the computational complexity of the algorithm is reduced and the convergence time of the algorithm is accelerated. In this paper, based on the alternating multiplier algorithm, the compressed perceptual magnetic resonance image is reconstructed by using Qu Bo transform and total variation as the regular term. This method can fully exploit the sparsity of different features of magnetic resonance images in different transform domains, and the reconstruction quality is improved on the basis of the same measurement matrix.
【學(xué)位授予單位】：哈爾濱理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：R445.2;TP391.41

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