GPU-based deep convolutional neural network for tomographic phase microscopy with ℓ1 fitting and regularization.

Tomographic phase microscopy (TPM) is a unique imaging modality to measure the three-dimensional refractive index distribution of transparent and semitransparent samples. However, the requirement of the dense sampling in a large range of incident angles restricts its temporal resolution and prevents its application in dynamic scenes. Here, we propose a graphics processing unit-based implementation of a deep convolutional neural network to improve the performance of phase tomography, especially with much fewer incident angles. As a loss function for the regularized TPM, the ℓ1-norm sparsity constraint is introduced for both data-fidelity term and gradient-domain regularizer in the multislice beam propagation model. We compare our method with several state-of-the-art algorithms and obtain at least 14 dB improvement in signal-to-noise ratio. Experimental results on HeLa cells are also shown with different levels of data reduction.

Isotropic inverse-problem approach for two-dimensional phase unwrapping.

We propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total variation. One desirable feature of our method is its rotation invariance, which allows it to unwrap a much larger class of images compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real data obtained through the tomographic phase microscope. The proposed method can enhance the applicability and outreach of techniques that rely on quantitative phase evaluation.