Fig. 1. Schematic illustration of stitching. (a) A big speckle pattern is split into many subblocks, and each subblock has its own independent ${\mathrm{PSF}}_{k}$. In other words, the big speckle pattern is obtained by stitching all independent subblocks together. (b) The segmentation of a big speckle pattern $I$.

Fig. 2. Diagram of piecing together a series of speckle patterns ${\{{I}_{{t}_{k}}\}}_{k=1}^{n\times n}$ [shown as subfigure (a)] into (b) a big speckle pattern; the yellow square frame denotes a single speckle pattern ${I}_{{t}_{k}}$.

Fig. 3. Experimental setup. $u$ and $v$ are distances from the object and the camera to the scattering layer, respectively.

Fig. 4. Experimental results. Rows I, II, and III correspond to $R=10.8$, 5.4, and 3.6, respectively. (a) Examples of captured speckle patterns, and (b) the corresponding autocorrelations of (a). (c) The power spectra of (a), (d) the averaged power spectra, and (e) the images reconstructed from (d). (f) The stitched speckle patterns at different sampling ratios and numbers of frames: $R=10.8$, $4\times 4$ frames (row I); $R=5.4$, $8\times 8$ frames (row II); and $R=3.6$, $12\times 12$ frames (row III), respectively. (g) The corresponding power spectra of (f), and (h) the images reconstructed from (g). (II,i) The autocorrelation and (III,i) the frequency spectrum of (I,i), the object. The inserts in rows II and III, and columns (c), (d), and (h) show zoom-ins of the center dash squares.

Fig. 5. Simulation results of different stitching numbers at $R=2$. Row I. (a) A single original speckle pattern; and (b) 4, (c) 9, (d) 36, and (e) 64 original patterns stitched together equally in two directions. Row II. The autocorrelations corresponding to I. Row III. The respective images reconstructed. Row IV. The averaged power spectra of 1, 4, 9, 36, and 64 frames of the original patterns. Row V. The corresponding power spectra of row I. (f) The evolution of the correlation coefficient with stitching number $n$. In rows IV and V, all have the same spectrum range because of the same pixel pitch. However, the power spectra of the stitched patterns have a higher resolution determined by the array size, which can be seen clearly from the amplified dash squares.

Fig. 6. Simulation results of different sampling ratios $R$. Row I. (a) A speckle pattern at $R=8$, and stitched speckle patterns of different sampling ratios and numbers of frames: (b) $R=4$, $2\times 2$ frames; (c) $R=2$, $4\times 4$ frames; (d) $R=1$, $8\times 8$ frames; and (e) $R=0.8$, $10\times 10$ frames, respectively. Row II. Autocorrelations corresponding to I. Row III. Reconstructed images, respectively. Row IV. Averaged power spectra. Row V. Corresponding power spectra of I (b)–(e). (f) The evolution of the correlation coefficient versus sampling ratio $R$. Again, all power spectra in rows IV and V have the same spectral range but different resolutions.