Selfrec-Net: self-supervised deep learning approach for the reconstruction of Cherenkov-excited luminescence scanned tomography

Abstract

As an emerging imaging technique, Cherenkov-excited luminescence scanned tomography (CELST) can recover a high-resolution 3D distribution of quantum emission fields within tissue using X-ray excitation for deep penetrance. However, its reconstruction is an ill-posed and under-conditioned inverse problem because of the diffuse optical emission signal. Deep learning based image reconstruction has shown very good potential for solving these types of problems, however they suffer from a lack of ground-truth image data to confirm when used with experimental data. To overcome this, a self-supervised network cascaded by a 3D reconstruction network and the forward model, termed Selfrec-Net, was proposed to perform CELST reconstruction. Under this framework, the boundary measurements are input to the network to reconstruct the distribution of the quantum field and the predicted measurements are subsequently obtained by feeding the reconstructed result to the forward model. The network was trained by minimizing the loss between the input measurements and the predicted measurements rather than the reconstructed distributions and the corresponding ground truths. Comparative experiments were carried out on both numerical simulations and physical phantoms. For singular luminescent targets, the results demonstrate the effectiveness and robustness of the proposed network, and comparable performance can be attained to a state-of-the-art deep supervised learning algorithm, where the accuracy of the emission yield and localization of the objects was far superior to iterative reconstruction methods. Reconstruction of multiple objects is still reasonable with high localization accuracy, although with limits to the emission yield accuracy as the distribution becomes more complex. Overall though the reconstruction of Selfrec-Net provides a self-supervised way to recover the location and emission yield of molecular distributions in murine model tissues.

Fig. 1.

The framework of the developed Selfrec-Net. (a) Schematic for CELST reconstruction, and (b) details of the reconstruction Selfrec-Net network.

Fig. 2.

The illustration of the phantom and the corresponding finite element mesh used in the experiments. (a) XFM-2 phantom, (b) the finite element mesh used in forward modeling, and (c) the placement of detectors.

Fig. 3.

Result illustrations when for a single target located in different depths. (a)-(d) are the reconstructed results by Tikhonov, Graph-TV, DSL, and Selfrec-Net methods for the depth of target is 6 mm, 8 mm, 10 mm and 12 mm, in turn. Intensity profiles are viewed along the z-axis direction (yellow dotted line in the second row), while the small red circles in 2D images represent the actual positions of the target.

Fig. 4.

Experimental results on the size of target for four algorithms. (a) MSE, (b) PSNR, and (c) SSIM.

Fig. 5.

CELST reconstruction results with the DSL and the Selfrec-Net under 3% and 5% noise. (a)-(d) 3D rendering of the reconstructed distribution of quantum yield and the corresponding 2D cross-sections taken from the $X=50$ mm and $Y=65$ mm, respectively.

Fig. 6.

The heat map of quantitative results with different levels of noise and different depths. (a) MSE, (b) PSNR, and (c) SSIM.

Fig. 7.

Result illustrations for the EED decreases from 4 to 1 mm. (a)-(d) 3D rendering of the ground-truth images, the corresponding 2D cross-section, and intensity profiles.

Fig. 8.

Reconstructed results when targets locate at different depths. (a)-(d) are the results with decreased the edge-to-edge distance from 4 mm to 1 mm, respectively.

Fig. 9.

Reconstructed results with three targets. (a-d) are the results with the edge-to-edge distance of 2 mm or 1 mm.

Fig. 10.

CELST reconstructed images with experiment data. (a) Luminescent image was overlaid on the microCT image. (b)-(e) are the reconstructed results and the corresponding 2D cross-sections for the four considered algorithms, respectively.