论文标题
Elfpie：错误范围傅立叶ptychographic迭代引擎
ELFPIE: an error-laxity Fourier ptychographic iterative engine
论文作者
论文摘要
We present a simple but efficient and robust reconstruction algorithm for Fourier ptychographic microscopy, termed error-laxity Fourier ptychographic iterative engine (Elfpie), that is simultaneously robust to (1) noise signal (including Gaussian, Poisson, and salt & pepper noises), (2) problematic background illumination problem, (3) vignetting effects, and (4) misaligning of LED位置，无需校准或恢复这些系统错误。在Elfpie中，我们在特征提取/恢复的框架下嵌入了FPM的反问题，并提出了由全局二阶总变量正规化（Hessian正则化）正规化的新数据保真成本函数。成本函数的封闭形式的复合梯度将得出，并使用具有自适应学习速率的Adabelief优化器将其反向传播，以更新样品和系统学生功能的整个傅立叶光谱。在模拟数据和实验数据上测试了ELFPIE，并将其与最先进的（SOTA）算法进行了比较。结果表明，在不同的变性问题和实施效率下，在其他SOTA方法和其他SOTA方法中，Elfpie的优越性。通常，与SOTA方法相比，Elfpie对高斯噪声具有强大的功能，其噪声强度更大，盐和胡椒噪声更大，噪声强度更大，而Poisson噪声则具有10倍的噪声强度。 Elfpie能够重建高达2 mm的大LED位置未对准的高保真样品场。它还可以绕过所有SOTA方法未能重建样品模式的渐晕效应。通过并行计算，Elfpie能够比传统FPM快地成为K次，其中K是使用的LED数量。
We present a simple but efficient and robust reconstruction algorithm for Fourier ptychographic microscopy, termed error-laxity Fourier ptychographic iterative engine (Elfpie), that is simultaneously robust to (1) noise signal (including Gaussian, Poisson, and salt & pepper noises), (2) problematic background illumination problem, (3) vignetting effects, and (4) misaligning of LED positions, without the need of calibrating or recovering of these system errors. In Elfpie, we embedded the inverse problem of FPM under the framework of feature extraction/recovering and proposed a new data fidelity cost function regularized by the global second-order total-variation regularization (Hessian regularization). The closed-form complex gradient for the cost function is derived and is back-propagated using the AdaBelief optimizer with an adaptive learning rate to update the entire Fourier spectrum of the sample and system pupil function. The Elfpie is tested on both simulation data and experimental data and is compared against the state-of-the-art (SOTA) algorithm. Results show the superiority of the Elfpie among other SOTA methods, in both reconstruction quality under different degeneration issues, and implementation efficiency. In general, compared against SOTA methods, the Elfpie is robust to Gaussian noise with 100 times larger noise strength, salt & pepper noise with 1000 times larger noise strength, and Poisson noise with 10 times noise strength. The Elfpie is able to reconstruct high-fidelity sample field under large LED position misalignments up to 2 mm. It can also bypass the vignetting effect in which all SOTA methods fail to reconstruct the sample pattern. With parallel computation, the Elfpie is able to be K times faster than traditional FPM, where K is the number of used LEDs.
