Statistical Applications of Maximized Likelihood Estimates with the Expectation-Maximization Algorithms for Reconstruction and Segmentation of MicroPET and Spotted Microarray Images
Tai Been Chen
Henry Horng-Shing Lu
|摘要:||正子斷層掃描影像(PET)針對功能性疾病診斷提供非侵入式且可量化等資訊；然而PET影像品質與使用的重建演算法有很高的相依性。屬疊代法之最大概似期望最大法(MLEEM)正快速成為PET影像重建的標準方法。常見的MLEM演算法對於隨機事件修正是採用二個Poisson分配相減(即: Prompt與delay資料相減)，此方法將失去Poisson分配的特性。我們將提出可行的演算法解決此一問題。利用聯合Poisson分配(即聯合Prompt與delay)做隨機事件修正並同時重建PET影像，稱之為PDEM演算法；不僅保持了Poisson分配特性而且不會增加估計隨機事件修正後的變異。利用模擬、實驗假體及實際老鼠等資料，採用變異係數和半高全寬值比較FBP, OSEM以及PDEM之影像重建品質。經由PDEM所得的影像品質均優於FBP或OSEM。
另一應用是對微陣列針狀基因影像之切割；該影像能提供生物醫學之基因資訊。此應用使用高斯混合模型以及無母數的核密度估計等方法用來切割雙色微陣列針狀基因影像。16片雙色基因影像設計嵌入已知濃度之 spike spots、重複Spots及染劑互換等實驗，將用以驗證與評估所提方法之有效性與正確性；結果顯示所提之方法不僅能有效切割Spots同時對Spots的估計具有高準確性。|
Positron emission tomography (PET) can provide in vivo, quantitative and functional information for the diagnosis of functional diseases; however, PET image quality is highly dependent on a reconstruction algorithm. Iterative algorithms, such as the maximum likelihood expectation-maximization (MLEM) algorithm, are rapidly becoming the standards for image reconstruction in emission tomography. The conventional MLEM algorithm utilized the Poisson model, which is no longer valid for delay-subtraction after random correction. This study was undertaken to overcome this problem. The MLEM algorithm is adopted and modified to reconstruct microPET images with random correction from the joint Poisson model of prompt and delay sinograms; this reconstruction method is called PDEM. The proposed joint Poisson model preserves Poisson properties without increasing the variances of estimates associated with random correction. The coefficients of variation (CV) and full width at half-maximum (FWHM) values were utilized to compare the quality of reconstructed microPET images of physical phantoms acquired by filtered backprojection (FBP), ordered subsets expectation-maximization (OSEM) and PDEM approaches. Experimental and simulated results demonstrated that the proposed PDEM method yielded better image quality results than the FBP and OSEM approaches. The segmentation of 3D microPET image is one of the most important issues in tracing and recognizing the gene activity in vivo. In order to discover and recover the activity of gene expression, reconstruction techniques with higher precision and fewer artifacts are necessary. To improve the resolution on microPET images, the PDEM method is applied. In addition, the advanced statistical technique based on the mixture model is developed to segment the reconstructed images. In this study, the new proposed method is evaluated with simulation and empirical studies. The performance shows that the proposed method is promising in practice. The segmentation of cDNA microarray spots is essential in analyzing the intensities of microarray images for biological and medical investigations. In this work, the nonparametric method of kernel density estimation is applied to segment two-channel cDNA microarray images. This approach successfully groups pixels into foreground and background. The segmentation performance of this model is tested and evaluated by sixteen microarrays. Specifically, spike genes with various levels of contents are spotted in a microarray to examine and evaluate the accuracy of the segmentation results. Duplicated design is implemented to evaluate the accuracy of the model. Swapped experiments of microarray dyes are also implemented. Results of this study demonstrate that this method can cluster pixels and estimate statistics regarding spots with high accuracy.
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