结合相位引导的Bregman TV正则化的近场全息断层成像联合重建
Joint Near-Field Holotomography Reconstruction with a Phase-Guided Bregman TV Regularization
AI总结：
该研究针对近场全息断层成像的非线性不适定逆问题，提出相位引导的Bregman TV正则化变分重建框架，在合成体模与实验数据上验证了其可实现稳定三维重建并改进吸收对比度恢复。
AI中文摘要：
近场全息断层成像将相干衍射成像与断层采集相结合，以恢复样本的三维复折射率。由于测得的衍射强度由非线性的物体传输和波传播过程产生，因此产生的逆问题本质上是非线性且不适定的。我们研究了一种基于完全非线性波传播模型的直接变分重建框架，该框架避免了中间相位检索和弱物体近似下的线性化。我们在合适的巴拿赫空间中分析了前向算子，确定了其弗雷歇可微性，并推导了变分重建的显式梯度表达式。为改进弱吸收特征的定量重建，我们进一步开发了相位引导的Bregman TV正则化框架，该框架利用相位与吸收分量之间的结构相关性，实现了多材料重建，无需对两个分量施加全局固定比例。我们在合成体模和实验数据上进行了数值研究，结果表明，与现有最优方法相比，该方法可实现稳定的三维重建，并改进了吸收对比度的恢复。
英文摘要：
Near-field holotomography combines coherent diffraction imaging with tomographic acquisition to recover the three-dimensional complex refractive index of a specimen. Since the measured diffraction intensities are generated by a nonlinear object transmission and wave propagation process, the resulting inverse problem is intrinsically nonlinear and ill-posed. We study a direct variational reconstruction framework based on a fully nonlinear wave propagation model that avoids both intermediate phase retrieval and linearization under the weak-object approximation. We analyze the forward operator in appropriate Banach spaces, establish its Fréchet differentiability, and derive explicit gradient expressions for variational reconstruction. To improve quantitative reconstruction of weak absorption features, we further develop a phase-guided Bregman TV regularization framework that exploits structural correlations between phase and absorption components. This enables multi-material reconstruction without imposing a globally fixed ratio between the two components. We perform numerical studies on synthetic phantoms and experimental data. The results demonstrate stable three-dimensional reconstructions and improved recovery of the absorption contrast compared to state-of-the-art methods.
