论文标题
部分可观测时空混沌系统的无模型预测
3D Reconstruction of unstained cells from a single defocused hologram
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
We investigate the problem of 3D complex field reconstruction corresponding to unstained red blood cells (RBCs) with a single defocused off-axis digital hologram. We employ recently introduced mean gradient descent (MGD) optimization framework, to solve the 3D recovery problem. While investigating volume recovery problem for a continuous phase object like RBC, we came across an interesting feature of the back-propagated field that it does not show clear focusing effect. Therefore the sparsity enforcement within the iterative optimization framework given the single hologram data cannot effectively restrict the true object volume. For phase objects, it is known that the amplitude contrast of the back-propagated object field at the focus plane is minimum and it increases at the defocus planes. We therefore use this information available in the detector field data to device weights as a function of inverse of amplitude contrast. This weight function is employed in the iterative steps of the optimization algorithm to assist the object volume localization. The experimental illustrations of 3D volume reconstruction of the healthy as well as the malaria infected RBCs are presented. The proposed methodology is simple to implement experimentally and provides an approximate tomographic solution which is axially restricted and is consistent with the object field data.