IEEE Trans Biomed Eng. 2019 Sep;66(9):2470-2480. doi: 10.1109/TBME.2018.2890410. Epub 2019 Jan 1.
The multiplicative regularization scheme is applied to three-dimensional electrical impedance tomography (EIT) image reconstruction problem to alleviate its ill-posedness.
A cost functional is constructed by multiplying the data misfit functional with the regularization functional. The regularization functional is based on a weighted L-norm with the edge-preserving characteristic. Gauss-Newton method is used to minimize the cost functional. A method based on the discrete exterior calculus (DEC) theory is introduced to formulate the discrete gradient and divergence operators related to the regularization on unstructured meshes.
Both numerical and experimental results show good reconstruction accuracy and anti-noise performance of the algorithm. The reconstruction results using human thoracic data show promising applications in thorax imaging.
The multiplicative regularization can be applied to EIT image reconstruction with promising applications in thorax imaging.
In the multiplicative regularization scheme, there is no need to set an artificial regularization parameter in the cost functional. This helps to reduce the workload related to choosing a regularization parameter which may require expertise and many numerical experiments. The DEC-based method provides a systematic and rigorous way to formulate operators on unstructured meshes. This may help EIT image reconstructions using regularizations imposing structural or spatial constraints.
将乘法正则化方案应用于三维电阻抗断层成像（EIT）图像重建问题，以减轻其不适定性。
通过将数据拟合函数与正则化函数相乘来构建代价函数。正则化函数基于具有边缘保持特性的加权 L-范数。采用高斯-牛顿法最小化代价函数。引入基于离散外演算（DEC）理论的方法，以在非结构网格上对正则化进行离散梯度和散度算子的公式化。
数值和实验结果均表明该算法具有良好的重建准确性和抗噪声性能。使用人体胸部数据的重建结果表明在胸部成像中具有很好的应用前景。
乘法正则化可应用于 EIT 图像重建，在胸部成像中具有很好的应用前景。
在乘法正则化方案中，不需要在代价函数中设置人工正则化参数。这有助于减少与选择正则化参数相关的工作量，而选择正则化参数可能需要专业知识和大量数值实验。基于 DEC 的方法为在非结构网格上对算子进行公式化提供了系统而严格的方法。这可能有助于使用施加结构或空间约束的正则化进行 EIT 图像重建。
