Three-dimensional tomography of red blood cells using deep learning

Joowon Lim,Ahmed B Ayoub,Demetri Psaltis

doi:10.1117/1.ap.2.2.026001

Joowon Lim, Ahmed B Ayoub + Show 1 more

Open Access

https://doi.org/10.1117/1.ap.2.2.026001

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Abstract

We accurately reconstruct three-dimensional (3-D) refractive index (RI) distributions from highly ill-posed two-dimensional (2-D) measurements using a deep neural network (DNN). Strong distortions are introduced on reconstructions obtained by the Wolf transform inversion method due to the ill-posed measurements acquired from the limited numerical apertures (NAs) of the optical system. Despite the recent success of DNNs in solving ill-posed inverse problems, the application to 3-D optical imaging is particularly challenging due to the lack of the ground truth. We overcome this limitation by generating digital phantoms that serve as samples for the discrete dipole approximation (DDA) to generate multiple 2-D projection maps for a limited range of illumination angles. The presented samples are red blood cells (RBCs), which are highly affected by the ill-posed problems due to their morphology. The trained network using synthetic measurements from the digital phantoms successfully eliminates the introduced distortions. Most importantly, we obtain high fidelity reconstructions from experimentally recorded projections of real RBC sample using the network that was trained on digitally generated RBC phantoms. Finally, we confirm the reconstruction accuracy using the DDA to calculate the 2-D projections of the 3-D reconstructions and compare them to the experimentally recorded projections.

Highlights

When we look at a three-dimensional (3-D) object in a conventional microscopy, we can only see a two-dimensional (2-D) projection at one time
We presented a deep neural network (DNN) approach for reconstructing tomograms of red blood cells (RBCs) with greatly improved image quality and super-resolution capability, especially enhancing the axial resolution
We digitally generated various RBCs and used them to generate synthetic measurements using the discrete dipole approximation (DDA) to overcome the lack of the ground truth

Summary

Introduction

When we look at a three-dimensional (3-D) object in a conventional microscopy, we can only see a two-dimensional (2-D) projection at one time. With coherent detection, a z-scan does not provide extra information compared to the single 2-D recording Another dimension that can be exploited is the illumination angle θ. ODT provides 3-D refractive index (RI) distributions[1] that contain morphological and biochemical information, which have been widely used to study various biological samples, which are summarized in recent review papers.[2,3,4,5] Under the assumption of weak scattering, multiple 2-D measurements in ðx; y; θÞ can be directly inverted to yield the 3-D RI information in ðx; y; zÞ using the Wolf transform,[6] which is the transformation that maps the spatial frequencies of the 2-D spectrum of the projections to the spatial frequencies of the 3-D spectrum of the object. Direct inversion reconstruction methods based on the Wolf transform suffer from the missing cone problem—a consequence of the missing spatial frequencies that are not accessible due to the limited NAs of the optics.[7]

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