Fig. 1. Schematic diagram of the physics enhanced deep learning approach for SPI. (a) The physics-informed DNN. (b) The SPI system. (c) The model-driven fine-tuning process. The face images were taken from CelebAMask-HQ [28].

Fig. 2. Diagram of the DNN structure we designed. It consists of an encoder path that takes the low-quality image reconstructed by DGI as its input and a decoder path that outputs an enhanced one.

Fig. 3. Comparative study of the proposed method with some other fast SPI algorithms with a low sampling ratio (β=1024/16384=6.25%). (a) The images reconstructed by HSI [14], TV [31], FDRI [35], DCAN [20], DGI with and without learned patterns illumination, physics-informed DNN, and the fine-tuning process. (b) PSNR and (c) SSIM of the reconstructed images are used to quantitatively evaluate the performance of different methods under different SNR levels. The PSNR and SSIM metrics were averaged over 30 randomly selected images from the test set. The face image was selected from CelebAMask-HQ [28].

Fig. 4. Convergence behavior of different error functions that measure (a) the objective function, (b) the prediction error, and (c) the error between the estimated bucket signal and the ideal one.

Fig. 5. Experimental results. The images reconstructed by DGI alone, DGI with physics-informed DNN, and the fine-tuning method. The sampling ratio β=6.25%.

Fig. 6. Experimental results: images of the badge of our institute reconstructed by (a) HSI with β=100% (it serves as the ground truth), (b) HSI with β=6.25%, (c) DCAN, (d) TVAL3, (e) fine-tuning with random initialization, (f) DGI with learned patterns, (g) DGI with physics-informed DNN, and (h) the fine-tuning process.

Fig. 7. Experimental results for single-pixel LiDAR. (a) Schematic diagram of the single-pixel LiDAR system. (b) Satellite image of our experiment scenario. The inset in the top left is the target imaged by a telescope, whereas the one in the bottom right is one of the echoed light signals. (c) Six typical 2D depth slices of the 3D object reconstructed by DGI with the learned patterns illumination, GISC [5], and the proposed fine-tuning method. (d) 3D images of the object reconstructed by the three aforementioned methods.