# Impact of Iterative Bilateral Filtering on the Noise Power Spectrum of Computed Tomography Images
## 4 Discussion  
This study aims to describe the characteristics of bilateral filters in filtering noise at various frequencies and their patterns in iterative filtering. We used the 1D NPS to characterize image noise. Previous studies that have been carried out have only explored the implementation of bilateral filters without iteration [21; 32; 39]. Bilateral filters increasingly suppress noise with each iteration. Figure 7, Figure 10, and Figure 13 show that with five iterations, the bilateral filter can suppress noise by more than 50%. This was observed in a homogeneous image with a homogeneous distribution of noise. Observations on areas with objects of various attenuations still need to be evaluated in the future. [PERSON] et al. (2020) investigated several filter algorithms, including bilateral filters, using an in-house point phantom. Their results showed that bilateral filters can \begin{table}
\begin{tabular}{c c} \hline \hline
**Filter Iteration** & **SSIM** \\ \hline
1 & 0.85 \\
2 & 0.69 \\
3 & 0.60 \\
4 & 0.54 \\
5 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Similarity index (SSIM) for each filter iteration. Figure 16: Anthropomorphic phantom images were filtered using a bilateral filter. (**a**) Original image, filtered image in (**b**) 1, (**c**) 2, (**d**) 3, (**e**) 4, and (**f**) 5 times iterations. Figure 15: Measurement of noise in the head anthropomorphic phantom image. (**a**) Noise level, (**b**) percentage of reduced noise. reduce noise by up to 18% for a single filter iteration, compared to the adaptive mean filter (AMF) which reduced noise by up to 29%, and the selective mean filter (SMF) which reduced it by up to 27%. The bilateral filter is not as aggressive as these other filters in reducing noise, but it maintains better spatial resolution [9]. Apart from the reduced noise magnitude, the texture also changes. The data showed interesting properties of bilateral filters in changing the noise texture. In the original images with tube currents of 77, 154, and 231 mAs, the NPS showed the peak frequency was about 0.2 mm\({}^{-1}\). When the images were filtered five times, the peak frequency shifted to lower values (Figures 6, 9 and 12). This phenomenon shows that the bilateral filter suppresses noise at high frequencies more aggressively than noise at low frequencies. By the fifth iteration, the NPS curve showed a flattening of its shape at frequencies above 0.2 mm\({}^{-1}\). The loss of high-frequency noise caused the bilateral filters to suppress soft (i.e., smooth) textures. In an image with visible gradation, this behavior will give the appearance of a staircase effect, and make the image less realistic. There are several extensions and variants of the bilateral filter that have been developed to deal with this effect [13; 40]. Notwithstanding, the bilateral filter shows very good results in reducing noise in general, especially in maintaining object edges when compared to other linear filters such as the mean filters and Gaussian filters. This was confirmed by the MTF50 and MTF10 obtained from the phantom edge which did not change significantly with filter iteration for all tube currents (Tables 3-5). This is an advantage of bilateral filters in clinical practice, where most filter algorithms tend to limit the spatial resolution to be able to suppress the noise. This was verified by testing the anthropomorphic phantom images. Behavior similar to that with the homogeneous phantom was observed, with noise decreasing with filter iteration (Figure 15). In the fifth iteration, noise is reduced by more than 60% (i.e., from 4.39 to 1.51 HU) in the frontal lobe area. In addition, the bilateral filter did not show aggressive behavior towards the edges of objects. In Figure 16, the edge between bone and soft tissue still looks sharp until the fifth iteration. There are no blurred edges or reverse effects. However, an unnatural appearance can be observed in the homogeneous areas of soft tissue. This causes the SSIM to decrease with increasing filter iterations.