北京生物醫(yī)學(xué)工程

基于投影矩陣廣義逆的CT重建迭代算法

Novel iterative algorithm for CT reconstruction based on theMoore-Penrose inverse of projection matrix

作者：王會(huì) 徐亞楠武王將石宏理楊智羅述謙

單位：首都醫(yī)科大學(xué)生物醫(yī)學(xué)工程學(xué)院(北京100069)

分類(lèi)號(hào)：R318.04

出版年·卷·期（頁(yè)碼）：2017·36·3（251-256）

摘要：

目的在CT檢查時(shí)，有限角度投影和稀疏矩陣投影能夠減少X射線的劑量，然而這會(huì)導(dǎo)致投影數(shù)據(jù)不足，給圖像重建帶來(lái)一定的困難。為了克服這一難題得到較好的重建圖像，本文提出一種基于計(jì)算投影矩陣廣義逆的CT迭代重建算法。方法該算法在計(jì)算過(guò)程中，將重建圖像表示為投影矩陣以及其廣義逆的乘積。首先使用一階迭代計(jì)算廣義逆矩陣，但是由于投影矩陣和其廣義逆矩陣都比較大，在迭代過(guò)程中以投影和濾波反投影代替。然后通過(guò)不同的算法分別對(duì)平行束投影、有限角度投影、稀疏矩陣投影的數(shù)據(jù)進(jìn)行重建，并對(duì)重建結(jié)果的均方差、通用圖像質(zhì)量指標(biāo)以及圖像互信息進(jìn)行比較。結(jié)果本文提出的方法重建出圖像的均方差、通用圖像質(zhì)量指標(biāo)和圖像互信息更優(yōu)，而且重建時(shí)間較短。結(jié)論該方法能夠在沒(méi)有未知圖像先驗(yàn)結(jié)構(gòu)信息和偽影猜想的情況下有效地提高重建圖像的質(zhì)量，而且該算法不需要計(jì)算投影過(guò)程，重建過(guò)程簡(jiǎn)單易行。

Objective In the CT examination, the limited-angle projection and sparse projection methods can be used to reduce the X-ray dose. However, these methods would result in the deficiency of the projection data and bringing certain difficulty for image reconstruction. For the purpose of overcoming the challenges and obtaining a higher quality reconstruction image, a new CT reconstruction method is proposed in this paper. Methods In the proposed method, the reconstruction image was expressed as the multiplication of projection matrix and its the Moose-Penrose pseudo-inverse. The first-order recursive formula was used to calculate the pseudo-inverse. However, the projection matrix and its the Moose-Penrose pseudo-inverse were replaced by projection and filtered back projection in the iterative process because of the difficulty of calculation. Then, the data of the parallel beam projection, the limited-angle projection and the sparse projection were reconstructed by different methods, and the mean square error (MSE), universal quality index (UQI) and mutual information (MI) were used to compare the results of the reconstruction images. Results The results of the MSE, UQI and MI by using the proposed method were better, and the time was less. Conclusions The proposed method can improve the quality of the reconstruction image efficiently without any prior structure information or an artificial assumption on the underlying image. Neither does it need the expression of projection process. The implementation of the proposed method is simple.

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