## 3 Experiment with the Complex Structures in the Tissue-Equivalent Phantom
The contrast improvement ratio (CIR) [35] serves as a metric to evaluate the effectiveness of different image processing techniques across 360 rotation angles of an object, as depicted in Figure 10. The orange line in the graph represents the CIR of the deconvolution method employing the PSF function, the purple line indicates the CIR of the proposed method, and the red line signifies the percentage improvement between these two methods. A notable observation from this graph is the similar trend exhibited by both methods, particularly their lowest CIR values at the 90 and 270-degree rotation angles. This similarity in the CIR trend and specific low points at these angles can be attributed to several factors. First, these angles typically correspond to the longest path lengths through the object, potentially leading to increased scattering and reduced contrast. Second, the alignment of certain features within the object's structure at these angles might amplify the scattering effects, further diminishing contrast. The consistency of this trend across both methods suggests that these dips in CIR are likely due to the inherent geometry and optical properties of the object rather than the limitations of the image processing techniques. The percentage improvement metric allows for the following observations. The initial large difference at the first angle: a substantial difference in CIR at the first angle may indicate that one method significantly outperforms the other under specific imaging conditions, influenced by the initial orientation of the object relative to the imaging apparatus. Decrease to a minimum at the 90 th angle: The minimum CIR at the 90 th angle suggests reduced effectiveness for both methods, likely due to the structural or optical characteristics of the object that increase the scattering or reduce the contrast at this specific orientation. Increase to a maximum at the 180 th angle: the peak in CIR at the 180 th angle indicates a point of optimal performance for both methods, likely due to more favorable conditions for contrast enhancement. Decrease to minimum at the 270 th angle and increase towards the 180 th angle: The pattern of decreasing to another minimum at the 270 th angle, followed  
Figure 9: Scattering suppression in transillumination imaging at 90-deg orientation with size image \(530\times 530\) pixels (\(\mu_{s}^{\prime}=1.00\)/mm, \(\mu_{a}=0.01\)/mm): (**a**) observed image in clear medium, (**b**) observed image in a scattering medium, (**c**) result using the PSF deconvolution technique, (**d**) result using the proposed technique, and (**e**) the intensity profile lines in (**a–d**) at the 350 th pixel row. by an increase towards the 360 th angle, highlights the influence of the object's orientation and imaging conditions on the performance of the methods. The cyclic nature of this pattern implies that certain angles consistently present challenges or advantages for contrast enhancement. Figure 11 shows cross-sectional images at the mid-height of the upper object, each scaled to a resolution of 10 mm/120 pixels. In Figure 11a, the image obtained in a clear medium reveals an object width of 11.69 mm. Figure 11b shows the image in a scattering medium, where the scattering effects obscure the object's dimensions. Figure 11c demonstrates the application of the erasing template technique, yielding a reconstructed object width of 12.86 mm, corresponding to an error \(\delta=10.01\%\). This error suggests that while the technique is beneficial for enhancing image clarity, it may alter the perceived dimensions of the object. Finally, Figure 11d depicts the result of the proposed technique, with a reconstructed object width of 12.39 mm, and a reduced error \(\delta=5.98\%\). This reduced error indicates a higher fidelity in preserving the object's true dimensions while effectively mitigating scattering effects. Similarly, Figure 12 shows cross-sectional images in the middle height of the lower object, each scaled to 10 mm/120 pixels.