An Analysis of Mathematical Transformations and a Comparison of Numerical Techniques for Computation of High-Energy CW Laser Propagation in an Inhomogeneous Medium

Breaux, Harold J.

doi:10.21236/ad0783478

Cited by 2 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This section presents the BPM forward model, whose complete derivation can be found in Appendix A. Although, BPM is a standard technique in optics for modeling propagation of light in inhomogeneous media [10]- [14], it is less known in the context of signal reconstruction and inverse problems. We shall denote our nonlinear forward model by y = S(x), where the vector y ∈ C M contains the samples of the measured light-field, x ∈ R N is the discretized version of the refractive index, and S : R N → C M is the nonlinear mapping.…”

Section: Forward Modelmentioning

confidence: 99%

See 1 more Smart Citation

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Kamilov

Papadopoulos

Shoreh

et al. 2016

IEEE Trans. Comput. Imaging

166

131

View full text Add to dashboard Cite

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.

show abstract

Section: Forward Modelmentioning

confidence: 99%

“…popular technique in optics called beam propagation method (BPM), which is extensively used for modeling diffraction and propagation effects of light-waves [10]- [14]. Accordingly, BPM provides a more accurate model than its linear counterparts, especially when scattering effects cannot be neglected.…”

mentioning

confidence: 99%