基于最大后驗概率的PET圖像重建算法研究
發(fā)布時間：2018-09-04 17:17
【摘要】：正電子發(fā)射斷層成像(Positron Emission Tomography,PET)是繼計算機斷層成像(Computed Tomography,CT)和磁共振成像(Magnetic Resonance Imaging,MRI)之后應(yīng)用于臨床的一種新型影像技術(shù),現(xiàn)已廣泛地使用于腫瘤細(xì)胞的探測、心臟病的診斷、神經(jīng)和精神類疾病的診斷以及新藥物的開發(fā)等領(lǐng)域。PET成像的目的是得到一個放射性物質(zhì)在人體內(nèi)部的分布圖,因此,如何根據(jù)掃描數(shù)據(jù)來重建出高質(zhì)量的圖像,一直是PET領(lǐng)域的一個重要研究課題�？傮w來說,PET圖像重建算法可以分為解析法和迭代法兩類。解析法的代表是以中心切片定理和傅立葉變換為基礎(chǔ)的濾波反投影算法,它具有計算簡單,成像速度快等優(yōu)點。但是當(dāng)投影數(shù)據(jù)中含有大量噪聲時,解析法很難重建出令人滿意的圖像,從而會影響臨床診斷的效果。迭代法可以分為代數(shù)迭代法和統(tǒng)計迭代法兩類。其中,代數(shù)迭代法的工作原理與解析法類似,由于其在重建圖像的過程中較難引入各種物理成像條件及統(tǒng)計模型,因此很難重建出高質(zhì)量的圖像,故此方法在PET圖像重建中使用較少。統(tǒng)計迭代法建立在觀測數(shù)據(jù)的統(tǒng)計模型基礎(chǔ)上,能夠重建出高精度的重建圖像,是目前PET圖像重建中使用最廣泛的一種方法。統(tǒng)計迭代法中經(jīng)典的PET圖像重建算法有很多,如最大似然期望最大算法(Maximum Likelihood Expectation Maximized,MLEM)、有序子集期望值最大算法(Ordered Subset Expectation Maximization,OSEM)和最大后驗概率算法(Maximum A Posterior,MAP)等。本文的主要研究內(nèi)容是MAP算法,又稱為懲罰最大似然算法或Bayesian算法。本學(xué)位論文共五章,具體內(nèi)容安排如下:在第一章中,我們首先介紹了PET成像技術(shù)的背景及意義,然后回顧了PET圖像重建算法的歷史與發(fā)展概況,最后簡單地概述了本文的主要研究內(nèi)容與結(jié)構(gòu)安排。第二章是PET圖像重建算法的基礎(chǔ)理論知識部分,主要介紹了PET中的一些經(jīng)典重建算法及它們的優(yōu)缺點。剩下三章是本文的主要工作,所取得的研究成果如下所述。在第三章中,我們通過把各向異性中值擴散濾波器(Anisotropic Median-Diffusion,AMD)融合到中值根先驗算法(Median Root Prior,MRP)中,提出了一種新的Bayesian圖像重建算法。由于中值濾波器對高斯和Poisson兩種噪聲的抑制效果不明顯,所以MRP算法很難取得令人滿意的重建結(jié)果。新算法通過把AMD濾波器融合到MRP算法中,有效地抑制了重建圖像中的所有噪聲。模擬仿真實驗結(jié)果表明,新算法在抑制噪聲和保護(hù)邊緣兩方面取得了良好的折中,較大程度地提高了重建圖像的質(zhì)量。在第四章中,我們通過把AMD模型引入到PET圖像重建算法中,提出了一種基于懲罰最大似然的PET圖像重建算法。通過實驗比較可知,新算法能取得較好的重建結(jié)果。此外,跟類似算法相比(如MLEM-PDE),新算法由于吸收了AMD模型的優(yōu)點,參數(shù)設(shè)置簡單,迭代過程中對梯度閾值和擴散次數(shù)的值不敏感,實用性較強。在第五章中,我們通過把一種修正的全變分模型(Total Variation,TV)和MLEM算法結(jié)合起來,提出了一種新的基于懲罰最大似然的PET圖像重建算法。PET圖像中的噪聲主要是以Poisson噪聲為主,一些傳統(tǒng)的PET圖像重建算法,如MLEM、MRP和MAP等,它們對一般的加性噪聲有較好的抑制效果,但是對與信號相關(guān)的Poisson噪聲的抑制效果卻很不理想。新算法通過把PMTV模型(Poisson-modified Total Variation,PMTV)引入到MLEM算法中,有效地抑制了重建圖像中的Poisson噪聲,較大程度地提高了重建圖像的質(zhì)量。
[Abstract]:Positron Emission Tomography (PET) is a new imaging technique which has been used in clinic after Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). It has been widely used in tumor detection, heart disease diagnosis, neurological and psychiatric diseases. The purpose of PET imaging is to obtain a map of the distribution of radioactive substances in the human body. Therefore, how to reconstruct high-quality images from scanned data has always been an important research topic in the field of PET. There are two kinds of analytic methods. They are based on the central slice theorem and Fourier transform. They have the advantages of simple calculation and fast imaging speed. However, when there is a lot of noise in the projection data, it is difficult to reconstruct a satisfactory image by analytic method, which will affect the effect of clinical diagnosis. Algebraic iteration method and statistical iteration method are two kinds of methods. The principle of algebraic iteration method is similar to analytic method. Because it is difficult to introduce various physical imaging conditions and statistical models in the process of image reconstruction, it is difficult to reconstruct high-quality images, so this method is less used in PET image reconstruction. Based on the statistical model of measured data, it can reconstruct the reconstructed image with high precision, which is one of the most widely used methods in PET image reconstruction. Ordered Subset Expectation Maximization (OSEM) and Maximum A Posterior (MAP), etc. The main contents of this paper are MAP algorithm, also known as penalty maximum likelihood algorithm or Bayesian algorithm. In the second chapter, the basic theory of PET image reconstruction algorithm is introduced, and some classical reconstruction algorithms in PET and their advantages and disadvantages are introduced. The remaining three chapters are the following In the third chapter, we propose a new Bayesian image reconstruction algorithm by fusing anisotropic median diffusion filter (AMD) into Median Root Prior (MRP). The new algorithm can effectively suppress all the noises in the reconstructed image by fusing the AMD filter into the MRP algorithm. Simulation results show that the new algorithm achieves a good compromise between noise suppression and edge protection. In Chapter 4, we introduce AMD model into PET image reconstruction algorithm, and propose a PET image reconstruction algorithm based on penalty maximum likelihood. The experimental results show that the new algorithm can achieve better reconstruction results. In addition, compared with similar algorithms (such as MLEM-PDE), the new algorithm is more efficient. In Chapter 5, we propose a new PET image based on penalty maximum likelihood by combining a modified Total Variation (TV) with MLEM algorithm. The noise in PET image is mainly Poisson noise. Some traditional PET image reconstruction algorithms, such as MLEM, MRP and MAP, have good suppression effect on general additive noise, but the suppression effect on signal-related Poisson noise is not ideal. AlVariation (PMTV) is introduced into MLEM algorithm to suppress Poisson noise in reconstructed images and improve the quality of reconstructed images.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.41
[Abstract]:Positron Emission Tomography (PET) is a new imaging technique which has been used in clinic after Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). It has been widely used in tumor detection, heart disease diagnosis, neurological and psychiatric diseases. The purpose of PET imaging is to obtain a map of the distribution of radioactive substances in the human body. Therefore, how to reconstruct high-quality images from scanned data has always been an important research topic in the field of PET. There are two kinds of analytic methods. They are based on the central slice theorem and Fourier transform. They have the advantages of simple calculation and fast imaging speed. However, when there is a lot of noise in the projection data, it is difficult to reconstruct a satisfactory image by analytic method, which will affect the effect of clinical diagnosis. Algebraic iteration method and statistical iteration method are two kinds of methods. The principle of algebraic iteration method is similar to analytic method. Because it is difficult to introduce various physical imaging conditions and statistical models in the process of image reconstruction, it is difficult to reconstruct high-quality images, so this method is less used in PET image reconstruction. Based on the statistical model of measured data, it can reconstruct the reconstructed image with high precision, which is one of the most widely used methods in PET image reconstruction. Ordered Subset Expectation Maximization (OSEM) and Maximum A Posterior (MAP), etc. The main contents of this paper are MAP algorithm, also known as penalty maximum likelihood algorithm or Bayesian algorithm. In the second chapter, the basic theory of PET image reconstruction algorithm is introduced, and some classical reconstruction algorithms in PET and their advantages and disadvantages are introduced. The remaining three chapters are the following In the third chapter, we propose a new Bayesian image reconstruction algorithm by fusing anisotropic median diffusion filter (AMD) into Median Root Prior (MRP). The new algorithm can effectively suppress all the noises in the reconstructed image by fusing the AMD filter into the MRP algorithm. Simulation results show that the new algorithm achieves a good compromise between noise suppression and edge protection. In Chapter 4, we introduce AMD model into PET image reconstruction algorithm, and propose a PET image reconstruction algorithm based on penalty maximum likelihood. The experimental results show that the new algorithm can achieve better reconstruction results. In addition, compared with similar algorithms (such as MLEM-PDE), the new algorithm is more efficient. In Chapter 5, we propose a new PET image based on penalty maximum likelihood by combining a modified Total Variation (TV) with MLEM algorithm. The noise in PET image is mainly Poisson noise. Some traditional PET image reconstruction algorithms, such as MLEM, MRP and MAP, have good suppression effect on general additive noise, but the suppression effect on signal-related Poisson noise is not ideal. AlVariation (PMTV) is introduced into MLEM algorithm to suppress Poisson noise in reconstructed images and improve the quality of reconstructed images.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.41
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