使用區塊式壓縮感知法之三維EIT影像重建研究

Abstract

電阻抗斷層影像(EIT)是一個成像速度快、造價低的非侵入式人體檢測的技術，它的目標為量測體內組織間電特性的差異，從而產生阻抗變化的影像，本論文旨在解決三維EIT影像重建上的巨大計算量以及解決EIT本身欠定的問題，藉由使用壓縮感知的技術提出一個降低重建時間和記憶體使用量的改良方法。首先，對龐大的電極數得到的龐大測量資料使用區塊式取樣，這將大幅降低Jacobian矩陣的大小和將可以使用更多的電極改善重建的精確度；再來加入一個門檻值限制方法，使Jacobian矩陣變為稀疏的形式，將矩陣中不重要的值變為零，在不影響影像品質的前提下，設門檻值為0.5，可使矩陣的大小與它矩陣中非零數目的比值達到53.94%，降低了約50%的矩陣大小；最後建立壓縮感知與EIT之間的關係，將壓縮感知為基於二步迭代收縮/門檻值的演算法和加入區塊式概念引進EIT影像重建的演算法中。由實驗結果可證明本論文提的區塊式壓縮感知法可以有效的解決三維EIT龐大的運算量，在電極數為72的三維EIT系統中，我們的方法與只有單純壓縮感知法相比，記憶體可以省下約61%的儲存空間，重建時間降低了約72%的時間，且電極數越多改善的差異越明顯，且此方法不只降低重建時間和記憶體使用量，它相對其他影像重建的方法可以更好的去抵抗雜訊，以及重建出比較好的影像解析度。

Electrical impedance tomography (EIT) is a fast and cost-effective technique that provides a tomographic conductivity image of a subject from boundary current–voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT image reconstruction problem and solving ill-posed linear inverse problem. First, we use block-based sampling for a large number of measured data from a large number of electrodes. This method will reduce the size of Jacobian matrix and can improve accuracy of reconstruction by using more electrodes. And then, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Finally, we built up the relationship between compressed sensing and EIT definitely and induce the CS- Two-step Iterative Shrinkage/Thresholding and block-based method into EIT image reconstruction algorithm. The result shows block-based compressed sensing enables the large scale 3D EIT problem to be efficiently. For a 72-electrode EIT system, our proposed method could save at least 61% of memory and reduce time by 72% than compressed sensing method only . The improvements will be obvious by using more the number of electrodes. And this method is not only better at anti-noise, but also faster and better resolution.