## 1 Introduction  
Sufficient oxygen supply in tissue is critical to maintaining its normal physiological functions [1, 2]. Local oxygen levels in tissue provide valuable insights into its health states, such as metabolic levels [3]. Oxygen is transported via binding to hemoglobin, the main protein of red blood cells, to different parts of the body, and is released to tissue through perfusion. Depending on the presence of binding oxygen molecules, hemoglobin can exist in two forms, oxygenated and deoxygenated hemoglobin, both of which exhibit distinct absorption properties in visible and near-infrared (NIR) ranges. Based on the differential absorption of hemoglobin, multispectral imaging was developed to quantify tissue perfusion properties, such as oxygen saturation [4]. However, the quantification accuracy was limited due to its inability to decouple tissue absorption from tissue scattering. Spatial frequency domain imaging (SFDI), on the other hand, independently evaluates tissue absorption and scattering properties [5, 6, 7]. SFDI uses 2D sinusoidal structured illumination to interrogate the samples. Tissue absorption and scattering modify the modulation of the illumination, and diffuse reflectance thus encodes the tissue's optical properties. To quantify tissue optical properties, typically, a set of three 2D sinusoidal patterns with a phase shift of 0\({}^{\circ}\), 120\({}^{\circ}\), and 240\({}^{\circ}\) are projected onto the sample surfaces sequentially, and corresponding images are acquired. Using the 3-phase demodulation technique, two images, often referred as AC and DC images, are derived. AC and DC images are calibrated to obtain modulation and reflectance images, which serve as searching indices of the pre-generated look-up tables (LUTs) to determine optical properties of the sample. Multispectral SFDI has been developed to map perfusion and hemodynamic properties of the tissue with an improved accuracy [8, 9]. Such quantification requiresimaging at multiple wavelengths (two wavelengths at least), typically in the red and near-infrared (NIR) range [10,11]. At each wavelength, a set of three phase-shifted patterns are projected onto the tissue surface and the corresponding reflectance images are acquired to determine the tissue's optical and perfusion properties [6].  
The overall process, however, is slow and limits the temporal resolution. In the past few years, significant efforts have been devoted to improving the imaging and quantification speed in SFDI imaging. Single snapshot SFDI reduced the number of required images from three to one [12, 13, 14], and look-up table (LUT)-based quantification significantly improved the quantification speed of optical property of the tissue [15]. For perfusion property quantification, the Beer-Lambert Law is the standard approach, which, however, can be slow for large images. To improve the speed for perfusion property quantification, artificial intelligence has been employed to train the predictive model based on a large set of training images [16,17].  
Despite recent advancements towards real-time mapping of tissue perfusion and hemodynamics, current methods are still limited by relatively slow processing speed, low image resolution, and the need for powerful computational hardware (e.g., a multi-GPU setup). This study aimed to develop a highly efficient LUT-based computational framework towards high-resolution real-time mapping of tissue perfusion and hemodynamics that can be implemented on cost-effective hardware platforms.