Fig. 1. Illustration of the proposed SSAI approach. (a) The scenario of imaging with strongly scattered light. The strongly scattering medium and the detector form a speckle imaging system. (b) Definition of the wavefront phase error in the speckle imaging system. (c) Implementation flowchart of the SSAI approach.

Fig. 2. Theoretical foundation for reconstructing the object phase spectrum in SSAI. The phase of the speckle spectrum autocorrelation is approximated to be equal to that of the object spectrum autocorrelation in the speckle imaging system.

Fig. 3. Recursive reconstruction path of the unit amplitude phasor of the object spectrum in SSAI. Each grid point represents a frequency point within the discrete frequency domain, denoted by the frequency vector f=(u,v). The arcs depict the recursive reconstruction path. The arrows on the arcs indicate the order of reconstruction. The reconstruction begins at (u,v)=(1,0), and the unit amplitude phasor at each f is reconstructed according to |f| from small to large in the counterclockwise direction. Here, only the early stages of the recursive path are displayed.

Fig. 4. Experimental setup of SSAI. BE, beam expander; RD, rotating diffuser; L, convex lens; DMD, digital micromirror device; DSM, dynamic scattering medium.

Fig. 5. Reconstruction results of stationary objects hidden behind a dynamic scattering medium via the SSAI approach proposed in this paper. (a) The original images of six different objects: “6,” “G,” “友,” “智,” “礼,” and “和.” (b) An unprocessed 512 pixel × 512 pixel speckle image of each object. (c) Reconstruction results via the popular SCI approach. (d) Reconstruction results via SSAI. mSSIM: modified structural similarity between the original object image and the reconstruction result.

Fig. 6. Reconstruction results of stationary objects via SSAI when using different numbers of speckle images. (a)-(e) Reconstruction results. The letter F below each reconstructed image indicates the number of original 512 pixel × 512 pixel speckle images used for the reconstruction. (f) The original images of two different objects.

Fig. 7. Reconstruction results of moving objects hidden behind a dynamic scattering medium via SSAI. (a) The object is moved to seven different positions on the object plane when speckle images are captured. (b)–(g) The reconstruction results of six different objects via SSAI.

Fig. 8. Reconstruction results of the object via SSAI under different horizontal object displacements, based on speckle images captured before and after the displacement. (a)–(e) Reconstruction results. The object displacements from left to right are −1, −0.5, 0, 0.5, and 1 mm, respectively. (f) The original images of two different objects.

Fig. 9. Reconstruction results of stationary objects hidden behind a dynamic scattering medium under background light interference via SSAI. (a) and (b) show the original images of the objects “友” and “2,” respectively. (a-1) and (b-1) show the 512 pixel × 512 pixel speckle images of the two objects captured under four SBR conditions, respectively. Reconstruction results of these objects via SCI and SSAI are shown in (a-2), (b-2) and (a-3), (b-3) respectively.

Fig. 10. Reconstruction results of moving objects hidden behind a dynamic scattering medium under background light interference via SSAI. (a-1) and (b-1) show speckle images captured at seven different object positions under two different intensities of background light interference, respectively. The average SBR of the speckle images captured at each object position is annotated under each speckle image. The value of mean SBR indicates the average SBR of all speckle images. (a-2) and (b-2) show the original object image. The reconstructed results via SCI under the two different intensities of background light are shown in (a-3) and (b-3). The reconstructed results via SSAI under the two different intensities of background light are shown in (a-4) and (b-4).

Fig. 11. Reconstruction results of size-scaling objects hidden behind a dynamic scattering medium via SSAI. (a) The object is scaled to three different sizes at different moments during the capture of speckle images. (b) Reconstructed images of objects “友,” “2,” and “S.”