## 4 Discussion  
In this study, we developed and demonstrated a highly efficient and accurate two-stage LUT method that quantifies the tissue's optical and perfusion properties with SFDI. High efficiency was achieved through direct index searching of two LUTs, which eliminated time-consuming fitting operations to determine optical and, subsequently, perfusion properties. GPU-based implementation significantly improved the searching speed through parallelization. At an image size of 2048 \(\times\) 2048 pixels, we achieved a quantification speed of 74 FPS for both optical and perfusion properties. In recent years, methods for direct quantification of optical and perfusion properties using artificial intelligence have been reported to improve the processing speed towards real-time applications. [PERSON] et al. reported a processing time of 94.4 ms (excluding time for image import and result display) for quantifying perfusion properties for images with a size of 540 \(\times\) 720 pixels using a deep residual network [17]. Using adversarial deep learning, [PERSON] and [PERSON] reported that approximately 40 ms was needed to determine optical and perfusion properties for images with a size of 512 \(\times\) 512 pixels [16]. It is worth noting that both studies utilized two wavelengths at around 660 and 850 nm, which are the same wavelengths as those used in this study. A two-stage LUT method is highly suitable for real-time applications. With GPU acceleration, it achieved 266 and 74 FPS for small and large sized images. The short processing time can provide ample room to accommodate more sophisticated algorithms while still maintaining real-time performance. When the two-stage LUT is coupled with a dual-sensor SFDI imaging system, reflectance images at 660 and 850 nm can be acquired simultaneously and processed rapidly, which would enable time-sensitive imaging applications, such as real-time tissue viability monitoring. Two-stage LUTs outperformed the Beer-Lambert Law-based quantification regardless of the computational platform. Even with GPU acceleration, the Beer-Lambert Law method only achieved 35.5 FPS for medium sized images. Any additional processing would slow it down to sub-30 FPS, which is not ideal for real-time applications. Although CPU-based implementation of two-stage LUT is not as fast, it does not require a dedicated GPU and offers a few advantages. First, the two-stage LUT is still suitable for offline applications where processing time is not a critical factor, and it is about 30% more efficient than the Beer-Lambert Law approach. Second, the two-stage LUT offered a processing speed of approximately 65 FPS for small sized images, which still could enable real-time applications when the image resolution is not a concern. It is worth noting that,  
Figure 6: Relative quantification error of (**A**) total hemoglobin concentration and (**B**) oxygen saturation between the designed values and the values obtained with the stage-2 LUT. in real-life applications, acquiring and transferring images to memory, and displaying the processed results, take additional time. To preserve the high performance of the two-stage LUT, a multi-threaded architecture could be adopted. Each thread runs independently and is only responsible for its own task, such as image transfer, quantification, or result display. The two-stage LUT quantification method presented in this study was intended to serve as a general framework to map the optical and perfusion properties of the tissue. Implementing this general framework requires additional considerations. Firstly, the optical property LUT was generated using MC simulation on homogenous phantoms. Homogenous phantom models have been widely used to generate LUTs for quantifying optical and physiological properties, and have yielded encouraging results. However, it is worth noting that building LUTs based on a more complex geometry, such as two-layer models, could further improve the accuracy and specificity of the quantification.