Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA.
IEEE Trans Med Imaging. 2010 Jan;29(1):44-54. doi: 10.1109/TMI.2009.2022540.
We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual-interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regularization shows improved ability to reconstruct sharp contrasts.
我们表明，基于全变差（TV）函数的正则化的电阻抗断层成像（EIT）图像重建算法适用于生理数据的体内成像。这种重建方法有助于保留重建轮廓中的不连续性，例如器官间边界处电特性的阶跃变化，这些变化通常会被传统的重建算法平滑掉。TV 函数的使用导致逆公式中不可微目标函数的最小化。这不能通过传统的优化技术（如牛顿法）有效地解决。我们探索了两种用于 TV 函数正则化的实现方法：滞后扩散方法和原始对偶内点方法（PD-IPM）。首先，我们阐明了这些算法在 EIT 重建中的实现细节。接下来，我们分析了这些算法在噪声模拟数据上的性能。最后，我们展示了用于通气和胃排空研究的体内数据的重建 EIT 图像。与传统的二次正则化相比，TV 正则化显示出更好的重建锐度对比的能力。
