Label-free tomographic phase microscopy is an excellent candidate to perform this task. High-throughput single-cell analysis is a challenging task. The proposed method is validated on both simulated and experimentally measured data. One of our key insights is that it is possible to obtain an explicit formula for computing the gradient of our nonlinear forward model with respect to the unknown object, thus enabling fast image reconstruction with the state-of-the-art fast iterative shrinkage/thresholding algorithm (FISTA). This expansion guarantees the convergence even for strongly scattering objects. Specifically, it corresponds to a series expansion of the scattered wave with an accelerated-gradient method. The proposed forward model can account for multiple scattering, which makes it advantageous in applications where linear models are inaccurate. In this paper, we describe a new technique-called Series Expansion with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for robust imaging under multiple scattering based on a combination of a new nonlinear forward model and a total variation (TV) regularizer. Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. An implementation of the proposed algorithm can be accessed and executed through a Code Ocean compute capsule. The processing of experimental data from synthetic aperture radar showed the capability for processing real images, including removing phase dislocations. When compared to the 2D windowed Fourier transform filter, SPUD performs better in terms of phase error and execution times. Simulation results with different levels of noise and wrapped phase fringe density reveal the suitability of the proposed method for accurate phase unwrapping and restoration. The proposed method relies on the least-squares Discrete Cosine Transform (DCT) solution for phase unwrapping with an additional sparsity constraint on the DCT coefficients of the unwrapped solution. In this paper, we present a non-iterative Simultaneous Phase Unwrapping and Denoising algorithm for phase imaging, referred to as SPUD. However, including a denoising stage increases the overall computational complexity resulting in long execution times. Recent methods for phase unwrapping in the presence of noise include denoising algorithms to filter out noise as a pre-processing stage.
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