Fig. 1. Process of reconstructing the original image by SH speckle. Different phase distribution of the image uploaded on FF beam will interact with the nonlinear scattering medium and generate a different SH speckle pattern. The original image and SH speckle patterns are fed into NSDN for joint training. The acquired SH speckle is fed into the learned NSDN to reconstruct the original image.

Fig. 2. NSDN architecture. Each box corresponds to a multichannel feature map. The number of channels is indicated at the top of each box, and the x–y size is provided at the left edge. The color of the boxes corresponds to different operation types, as listed in the lower-right corner of the figure. Arrows indicate the direction of data operations.

Fig. 3. Reconstruction of MNIST data set. (a) Prediction results of test MNIST data set and (b) the corresponding α and β evolution curves in the training process. (c) Prediction evolution results of MNIST data set, with corresponding values of α and β.

Fig. 4. Reconstruction of CIFAR data set. (a) Prediction results of test CIFAR data set and (b) the corresponding α and β evolution curves in the training process. (c) Prediction evolution results of CIFAR data set, with corresponding values of α and β.

Fig. 5. Verification of robustness of NSDN for different diffusers. (a) Scanning electron microscope image of LiNbO3 diffusers. (b) Reconstruction results for each data set using different diffusers, with each column corresponding to a specific diffuser.

Fig. 6. Reconstruction results of unseen class of MNIST and CIFAR data sets.

Fig. 7. Quantitative evaluation of the NSDN performance. 1st and 2nd represent different diffusers, respectively; M and C mean MNIST and CIFAR data set, respectively; US means using unseen classes as test data set. (a) Different diffusers. (b) Unseen classes.

Fig. 8. Preparation of lithium niobate powder film using electrophoresis.

Fig. 9. Schematic of the experimental setup. L1–L4, lenses, with focal lengths of 50, 200, 100, and 100 mm; BS, beam splitter; SLM, spatial light modulator; M1, mirror; Obj., objective; F, filter; CCD, charge coupled device camera. Inset: image loaded on the SLM.