Fig. 1. Incoherent scattering imaging experimental system. (1) and (2) are the captured scattered patterns (the raw data and corresponding partial contrast stretched map) with optical thickness of 8 and 16, respectively. Note that these data are recorded in two sets of experiments: (1) capture data by the camera directly; (2) capture data with two additional apertures placed before the camera. KLS, Köhler lighting system; P, polarizer; ambient light, generated by a high-power LED through a diffuse slate (the distance between the slate and the tank side was around 3.5 cm); camera, working with an imaging lens ($f=250\mathrm{mm}$, not shown in the figure). $d_1\simeq 41\mathrm{cm}$, $d_2\simeq 15\mathrm{cm}$. The 33.6 cm thick tank is equipped with fat emulsion diluent to simulate a dynamic scattering medium. Note that the scattered patterns shown in (2) look dimmed because a significant part of the large-angle scattered light has been blocked out.

Fig. 2. Optical thickness of intralipid suspensions with respect to its density. (b)–(j) Speckle patterns corresponding to different densities. Scale bar: 200 μm.

Fig. 3. Multiple scattering trajectories in dynamic media. In this illustration, scatterers move from the black circle to the blue circle during time interval $\mathrm{\Delta }\tau$, and $r_i(i=1,\dots ,n,\dots ,N)$ represents the location where scattering event occurs.

Fig. 4. Experiment setup. (a) Dual camera acquisition system. (b) Experimental site map of intralipid dilution: 11.47 L purified water ($33.6\mathrm{cm}\times 19.5\mathrm{cm}\times 17.5\mathrm{cm}$) and 2 mL intralipid 20%.

Fig. 5. Decorrelation curves for different concentrations of intralipid dilutions. The data points and the error bars represent the mean value and the standard error of the correlation coefficient calculated from 10 image pairs. The solid lines in different colors are the fitting results, and the corresponding intralipid volume $V_I$ and optical thickness (OT) are shown in the legend. Here, the coefficient of determination (R-square) is used to describe the goodness of fit. Note that the horizontal axis is logarithmic scale.

Fig. 6. Experimental results. (a) Ground truths, and the reconstructed images in the case that the optical thickness equals (b) 8 and (c) 16, respectively.

Fig. 7. Robustness against the position change of the object/camera. $\mathrm{\Delta }d$ is the displacement of the object/camera (in pixel). The data points and the error bars represent the mean values and the standard deviations of the SSIM/RMSE of 10 reconstructed images (digits ‘0–9’).

Fig. 8. Robustness against the scaling and rotation of the object/camera. $\beta$ is the scaling factor of the image size, $\mathrm{\Delta }\theta$ the rotation angle, and $C_g$ the image contrast gradient. The data points and the error bars in (a)–(d) represent the mean values and the standard deviations of the SSIM/RMSE of 10 reconstructed images (digits ‘0–9’). (e) and (f) SSIM/RMSE of digit ‘5’ with respect to $\mathrm{\Delta }\theta$ and $C_g$. (g) Visualized reconstructed digits.

Fig. 9. Reconstruction of nondigit objects with the neural network trained by using digits. (a) First and third rows are the ground truths; second and fourth are the corresponding reconstructed images. (b) Reconstructed USAF target and the highlight of some of its portions.

Fig. 10. Experimental results with natural scene object. (a) Scattered patterns. (b) Corresponding ground truth. (b) Reconstructed results.

Fig. 11. Proposed neural network architecture. (a) Digits in the format $m\text{−}n$ below each layer denote the number of input channels $m$, and the number of output channels $n$. (5, 5) and (3, 3) denote the size of the convolution kernel in pixel counts. (b) Detailed information of neural network structure.