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In measuring a transmission matrix (TM) of a scattering medium, the normal way requires projecting a large number of patterns, resulting in significant measurement time. Here, we propose to do imaging through scattering media using a path-planning-based downsampling TM. The proposed method is verified by measuring TMs for imaging through scattering media when Walsh, Cake-cutting, and Russian doll Hadamard transforms (HTs) are adopted. Based on the spectral characteristics of different HTs of natural images, corresponding sampling paths are artificially planned, which guarantees the method to preferentially measure components in TM in relation to the more important spectra. This means that our method can reduce the number of patterns during measurement, thus improving the imaging speed while only sacrificing a little imaging quality. Experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The memory‐effect‐based speckle auto‐correlation method has gained significant attention for its ability to perform single‐shot noninvasive imaging through scattering media. Despite its advantages, however, not only its imaging field‐of‐view (FOV) is limited by the memory effect (ME), but also the relative positions and orientations of the reconstructed objects beyond ME are lost. Therefore, an approach that enables the reconstruction of multiple objects or a whole object behind scattering media beyond the ME region while accurately preserving the relative positions and orientations of its sub‐objects is proposed. The method achieves this by directly leveraging the correlation of the collected speckle patterns. Experimental results validate the effectiveness of the proposed method. It not only can reconstruct the image of multiple objects or a whole object beyond the ME region simulated by a digital micromirror device but also can reconstruct the image of a fluorescent object beyond the ME region noninvasively, which is well consistent with the theoretical predictions. The method provides a promising pathway for noninvasively visualizing fluorescent objects behind scattering media without being constrained by ME, thereby expanding the imaging FOV. [ABSTRACT FROM AUTHOR]