Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Abstract

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear counterparts, but they generally result in computationally prohibitive reconstruction algorithms. Although sparsity-driven regularizers significantly improve the quality of reconstructed image, they further increase the computational burden of imaging. In this paper, we present a novel iterative imaging method for optical tomography that combines a nonlinear forward model based on the beam propagation method (BPM) with an edge-preserving three-dimensional (3-D) total variation (TV) regularizer. The central element of our approach is a time-reversal scheme, which allows for an efficient computation of the derivative of the transmitted wave-field with respect to the distribution of the refractive index. This time-reversal scheme together with our stochastic proximal-gradient algorithm makes it possible to optimize under a nonlinear forward model in a computationally tractable way, thus enabling a high-quality imaging of the refractive index throughout the object. We demonstrate the effectiveness of our method through several experiments on simulated and experimentally measured data.

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

“…We build the CNN, based on the forward model of light propagation, 21,23 to model the diffraction and propagation effects of light-waves. It is known that the scalar inhomogeneous Helmholtz equation completely characterizes the light field at all spatial positions in a time-independent form E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; 3 3 4 ½∇ 2 þ k 2 ðrÞuðrÞ ¼ 0;…”

“…By introducing the complex envelope aðrÞ of the paraxial wave uðrÞ ¼ aðrÞ expðjk 0 n 0 zÞ for BPM, we can obtain an evolution equation 21 in which z plays the role of evolution parameter E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 3 2 6 ; 6 0 7 aðx; y; z þ δzÞ ¼ e jk 0 δnðrÞδz…”

“…The beam propagation method (BPM) 20 is then applied in phase tomography to provide a more accurate model by considering the nonlinear light propagation with scattering. 21,22 And the multislice propagation modeling is definitely similar to the neural network in the field of machine learning. 23,24 By combining the nonlinear modeling and the sparse constraint in the gradient domain, the Psaltis group has validated the competitive capability of this learning approach over conventional methods.…”

“…23,24 By combining the nonlinear modeling and the sparse constraint in the gradient domain, the Psaltis group has validated the competitive capability of this learning approach over conventional methods. 21,23 Despite its success in modeling with l 2 -norm constraint, the current method is still a preliminary network, especially compared with the state-of-the-art deep learning frameworks, 25 and the iterative reconstruction is challenging to deploy in practice due to the high computational cost and the difficulty of the hyperparameter selection. More potential can be exploited in both optimization algorithms and better network architectures.…”

Learning from Examples in Optical Imaging

“…However, in order to surpass the current limits in term of resolution and penetration, multiple scattering has to be taken into account. A recently investigated approach is to build a digital model of the object, represented by its refractive index distribution, and to optimize it so that it matches the experimental measurements [4][5][6]. The physical forward model that relates the refractive index to the measured scatted field can be chosen so that it includes multiple scattering.…”