Fig. 1. Schematic and principles of compressed sensing (CS) reflection matrix optical coherence tomography (RM-OCT). (a) Schematic of the RM-OCT system: A laser centered at 790 nm serves as the light source, with a spatial light modulator (SLM) performing biaxial scanning by projecting phase patterns onto the target area. A CCD camera collects backscattered photons. (b) Principle of RM measurement based on CS: where Y is an observation matrix of size (m × n) with m < n, A is a measurement matrix of size (m × n), and RM is the reflectance matrix of size (n × n) to be solved.

Fig. 2. SVD of the reflection matrix and image reconstruction. (a) SVD: The reflection matrix (RM) is decomposed using singular value decomposition. Larger singular values correspond to single-scattering photons, while smaller values are associated with multiple-scattering photons. (b) Image reconstruction: Images of single scattering (I_ss) are reconstructed by applying the Hadamard product to the reshaped singular vectors, utilizing the selected singular values.

Fig. 3. Electric field Monte Carlo experiments are conducted to evaluate the effectiveness of CS in RM measurements. (a) Simulated “sandwich” structure sample with scattering properties. (b) Hidden USAF target pattern in the middle layer. (c) En face image of the sample under coherent illumination. (d) RM obtained via uniform sampling (51point×51point). (e) RM obtained from 50% random sampling. (f) Singular value distributions for (d) and (e). (g) Image reconstruction from uniform sampling. (h) Image reconstruction from 50% random sampling. (i) Intensity distributions along the white dashed lines in (g) and (h), comparing reconstruction quality.

Fig. 4. RM measurement at different sampling rates. (a) RM obtained through 30% random sampling. (b) RM obtained through 50% random sampling. (c) RM obtained through uniform sampling. (d) Singular value distribution of RM at different sampling rates, highlighting that, despite some differences at lower sampling rates, the major high singular values remain consistent. (e) Intensity distributions along the blue dashed lines in (a)-(c), showing signal recovery across different sampling rates. (f) Deviations in intensity from uniform sampling at the blue dashed line positions in (a)–(c), comparing the 30% and 50% random sampling rates with uniform sampling.

Fig. 5. RM-OCT imaging in scattering media. (a) The imaging sample, a housefly wing covered with subcutaneous chicken mucosa (approximately 20 µm thick) to introduce scattering effects. (b) The en face image of the sample, where the target information is overwhelmed by the scattered light field. (c) Intensity distribution along the black dashed line in (b), showing the effect of scattered light. (d) RM obtained using 50% compressed sampling. (e) RM obtained from uniform sampling. (f) Singular value distributions for the reflection matrices shown in (d) and (e), illustrating the impact of different sampling rates. (g) Image reconstruction using the top 1000 singular values from the RM obtained with 50% CS. (h) Image reconstruction using the top 1000 singular values from the RM obtained via uniform measurement. (i) Intensity distributions along the white dashed lines in (g) and (h), comparing image reconstruction quality between 50% CS and uniform sampling. Scale bar: 0.15 mm.