ABSTRACT

This work is concerned with the image reconstruction of the Jacobian-based linearized EIT problem. Based on the homotopy perturbation technology, we first propose a novel class of iteration schemes with different orders of approximation truncation (named as HPI for short), which contains Landweber-type iteration method. Afterwards, nonsmooth priors such as ${\ell }^1$-norm or total variation penalty are introduced with the proposed HPI method to improve the imaging quality. However, it is known that Landweber-type iteration method is the widely used imaging algorithm, but in its basic form, the imaging speed is slow and the imaging accuracy is low. Furthermore, Nesterov's strategy is conducted to accelerate the proposed approaches. Numerical simulations with synthetic dada are performed to validate that our proposed approaches have robustness to noise and can indeed improve the image resolution and the imaging speed. Especially, numerical results explicitly show that Nesterov's acceleration versions make significantly remarkable acceleration effects.

摘要

这项工作涉及基于 Jacobian 的线性化 EIT 问题的图像重建。基于同伦微扰技术，我们首先提出了一类新的具有不同近似截断阶数的迭代方案（简称HPI），其中包含Landweber型迭代方法。之后，非光滑先验，例如${\ell }^1$提出的HPI方法引入了-范数或总变异惩罚以提高成像质量。然而，众所周知，Landweber型迭代法是应用广泛的成像算法，但其基本形式成像速度慢，成像精度低。此外，Nesterov 的策略旨在加速所提出的方法。使用合成数据进行数值模拟以验证我们提出的方法对噪声具有鲁棒性，并且确实可以提高图像分辨率和成像速度。特别是，数值结果明确表明，Nesterov 的加速版本具有显着的加速效果。