# GPU Adding-Doubling Algorithm for Analysis of Optical Spectral Images
## 4 Discussion  
Our study has demonstrated that the AD algorithm matches the accuracy of the MC method while also being versatile and compatible with implementation on GPUs. The computational speed-up achieved by the GPU-accelerated AD algorithm when compared to the GPU MC method, ranges from about 5000 to 40,000 times faster. This remarkable improvement in computational efficiency allows for the entire hyperspectral image to be analyzed within minutes. While the MC method excels in capturing intricate photon interactions, its computational demands are often prohibitive for large-scale simulations. In contrast, the AD algorithm serves as a more efficient alternative, offering an analytical solution that strikes a balance between accuracy and computational efficiency. Based on our study results, we can conclude that a GPU-accelerated two-layer IAD provides an acceptably accurate, fast, and reliable approach for solving inverse scattering problems and extracting important tissue properties, such as scattering properties and chromophore concentrations. Our calculated skin reflectance values align closely with the measurements taken before, during, and after the cuff test. Additionally, the obtained tissue properties using the IAD approach effectively reflect the changes in tissue physiology. Figure 7: Colormaps of **(a)** tissue oxygenation and (b) the total hemoglobin concentration before, during, and after a cuff test. \begin{table}
\begin{tabular}{l l l l} \hline  & **Before** & **During** & **After** \\ \hline
**Tissue oxygenation (\%)** & \(58.57\pm 10.83\) & \(0.24\pm 2.11\) & \(92.91\pm 6.02\) \\ \hline
**Total hemoglobin (\%)** & \(0.54\pm 0.07\) & \(0.68\pm 0.09\) & \(1.11\pm 0.12\) \\ \hline \end{tabular}
\end{table} 
Table 8: Calculated mean values of tissue oxygenation and the total hemoglobin concentration before, during, and after the cuff test. In recent years, the use of GPUs has advanced computational efficiency and accelerated processing capabilities. In our study, we specifically focused on implementing the AD algorithm on GPUs to enhance computational speed further. Additionally, we combined the AD and LM algorithms on the GPU platform to extract object parameters from optical spectral data effectively. By harnessing the power of GPUs, we aimed to achieve improvements in the computational speed of AD calculations. This integration of GPU technology with the AD algorithm holds the potential to advance our understanding of light transport in biological tissues and can pave the way for more efficient simulations and clinical applications, either in HSI [27] or related biomedical optical applications [28; 29]. In our previous publication, we reported a GPU implementation of the diffuse approximation algorithm for analyzing hyperspectral images of skin [30]. Although this algorithm proved to be sufficiently fast in providing extracted tissue parameter maps in (almost) real-time, its primary limitation is that it is an approximation only, and therefore, the resulting maps differ from the true values. On the other hand, the AD algorithm is as accurate as the MC algorithm; thus, the extracted tissue properties correspond to the true values, as demonstrated in our recent publication [31]. Although real-time image processing has not been achieved yet, we believe that by reducing the number of the analyzed wavelengths, further optimizing the algorithm, and implementing it in more computationally efficient programming languages, we can attain real-time image analysis. This advancement would make HSI even more attractive for clinical applications. Our approach has an obvious limitation in that it operates under assumptions outlined by [PERSON] et al. [13], including the absence of time dependence, a geometric model comprising uniform layers of finite thickness extended infinitely parallel to the surface, uniform scattering and absorbing properties within tissue layers, and uniform illumination by collimated or diffuse light.