鍾孝文臺灣大學：電機工程學研究所許家碩Hsu, Jia-ShuoJia-ShuoHsu2007-11-262018-07-062007-11-262018-07-062007http://ntur.lib.ntu.edu.tw//handle/246246/53053本論文展示一種藉著利用半週期信號的各週期彼此間的關連性，以成像和重建動態影像的新技巧。由於一個動態物件的各張影像在其相對應k空間和時序上往往具有相當程度的關連性，是以往往可以藉由利用這一關連性重建以疏取樣的方式加速取得的影像。現有的一些加速技巧如UNFOLD和k-t BLAST正是利用此一時序和空間上的關連性，然而也往往受限於相位失真和重建高頻時帶來的過多錯誤。我們的成果顯示若是將原本用來表現一半週期信號的N維架構依其週期延伸成N+1維的架構，就有相當程度的機會能提升高頻重建的正確率。這個技巧在利用既有頻寬上也有著優於傳統方法的彈性，卻也比傳統方法對位移更加敏感。上述的現象可以藉由映射到球堆積問題來有效詮釋。這一建模的結果足以凸顯我們提出的UNPACK方法在利用半週期關連性上的便利性。將UNPACK應用在動態心臟影像時，可以取得在比用k-t BLAST更加正確的收縮期影像。這些結果也和我們稍早在理論上預測一致。是以只要利用半週期信號源本身的關聯性，就足以重建正確率更高的動態心臟影像。This thesis concerns a modified dynamic cardiac imaging and reconstruction technique (referred to as UNPACK throughout the thesis)that acquires and reconstructs the undersampled dynamic images exploiting inter-period cor- relations of quasi-periodic signals. Dynamic images of moving objects often exhibit significant correlation in their k-spaces and time, enabling improved temporal resolution through accelerated sampling of the dynamic object by acquiring undersampled images at the cost of aggravated aliasing. Developed methods such as UNFOLD and k-t BLAST de-alias these images by exploit- ing their spatiotemporal correlation, yet with inherent limitations inducing loss of phases and increased reconstruction error in high frequency compo- nents. Our work shows that by altering the conventional N-dimensional quasi-periodic representation into a N + 1 dimensional representation ac- cording to its periodicity, it is possible to obtain lower overall variances and higher reconstruction accuracy of high frequency components accompany- ing enhanced recovery of dynamics. It also demonstrates extra flexibility of bandwidth usage yet higher susceptibility to displacement, which can both be explained by mapping a portion of the targeting problems sphere-packing problem. This formulation shows that the modified formalism proposed in UNPACK facilitates the exploitation of intrinsic correlation in quasi-periodic signals. However, these improvements are achieved at the cost of increased susceptibility toward displacement as in previous methods. By implement- ing UNPACK on dynamic cardiac images, we are able to obtain images with improved dynamics and higher accuracy at systolic phases in comparison to those reconstructed with k-t BLAST. These results are consistent with our previous assumptions concerning improved high frequency performances. Therefore, it is possible to further recover the dynamics of dynamic cardiac images by exploit their inherent inter-period correlations.1 Introduction 6 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Dynamic MRI: a k-t Space Perspective 9 2.1 k-t space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Lattice Theoretic Analysis . . . . . . . . . . . . . . . . . . . . 10 2.3 Methodologies Exploiting Spatiotemporal Correlations . . . . 12 3 UNFOLD and k-t BLAST 14 3.1 UNFOLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 k-t BLAST and k-t SENSE . . . . . . . . . . . . . . . . . . . 17 3.3 Issues Remained Concerned . . . . . . . . . . . . . . . . . . . 19 4 UNPACK 21 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Inter-Period Correlations . . . . . . . . . . . . . . . . . . . . . 22 4.3 k-t-T Space: UNPACKing the Signals . . . . . . . . . . . . . . 24 5 Application: Dynamic Cardiac Imaging 26 5.1 Dynamic Cardiac Imaging . . . . . . . . . . . . . . . . . . . . 26 5.2 k-t BLAST on Dynamic Cardiac Imaging . . . . . . . . . . . . 27 5.2.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2.2 Materials and Methods . . . . . . . . . . . . . . . . . . 28 5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.3 UNPACK on Dynamic Cardiac Imaging . . . . . . . . . . . . 32 5.3.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.3.2 Materials and Methods . . . . . . . . . . . . . . . . . . 34 5.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.3.4 Discussion and Conclusion . . . . . . . . . . . . . . . . 36 6 Conclusion and Future Works 39 A 411398428 bytesapplication/pdfen-US動態影像UNFOLDk-t BLAST心臟週期間關連性疏取樣dynamic imagingcardiacinter-period correlationundersamplingthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53053/1/ntu-96-R94921058-1.pdf