基于改进迭代收缩阈值算法的微观3D重建方法

迭代收缩阈值算法（ISTA）求解离焦深度恢复动态优化问题时，采用固定迭代步长，导致算法收敛效率不佳，使得重建的微观3D形貌精度不高。为此，提出一种基于加速算子梯度估计和割线线性搜索的方法优化ISTA——FL-ISTA。首先，在每一次迭代中，由当前点和前一个点的线性组合构成加速算子重新进行梯度估计，更新迭代点；其次，为了改变迭代步长固定的限制，引入割线线性搜索，动态确定每次最优迭代步长；最后，将改进的迭代收缩阈值算法用于求解离焦深度恢复动态优化问题，加快算法的收敛速度、提高微观3D形貌重建的精度。在对标准500 nm尺度栅格的深度信息重建实验中，与ISTA、快速ISTA （FISTA）和单调快速ISTA （MFISTA）相比，FL-ISTA收敛速度均有所提升，重建的深度信息值下降了10个百分点，更接近标准500 nm栅格尺度；与ISTA相比，FL-ISTA重建的微观3D形貌均方差（MSE）和平均误差分别下降了18个百分点和40个百分点。实验结果表明，FL-ISTA有效提升了求解离焦深度恢复动态优化问题的收敛速度，提高了微观3D形貌重建的精度。

Microscopic 3D reconstruction method based on improved iterative shrinkage thresholding algorithm

Iterative Shrinkage Thresholding Algorithm (ISTA) often uses fixed iteration step to solve the dynamic optimization problem of depth from defocus, which leads to poor convergence efficiency and low accuracy of reconstructed microscopic 3D shape. A method based on gradient estimation of acceleration operator and secant linear search, called Fast Linear Iterative Shrinkage Thresholding Algorithm (FL-ISTA), was proposed to optimize ISTA. Firstly, the acceleration operator, which consists of the linear combination of the current and previous points, was introduced to reestimate the gradient and update the iteration point during each iteration process. Secondly, in order to change the restriction of the fixed iteration step, secant linear search was used to determine the optimal iteration step dynamically. Finally, the improved algorithm was applied to solve the dynamic optimization problem of depth from defocus, which accelerated the convergence of the algorithm and improved the accuracy of reconstructed microscopic 3D shape. Experimental results of reconstructed standard 500 nm grid show that compared with ISTA, FISTA (Fast ISTA) and MFISTA (Monotohy FISTA), the efficiency of FL-ISTA was improved and the depth from defocus decreased by 10 percentage points, which is closer to the scale of standard 500 nm grid. Compared with ISTA, the Mean Square Error (MSE) and average error of microscopic 3D shape reconstructed by FL-ISTA were decreased by 18 percentage points and 40 percentage points respectively. The experimental results indicate that FL-ISTA can effectively improve the convergence rate of solving the dynamic optimization problem of depth from defocus and elevate the accuracy of the reconstructed microscopic 3D shape.