## 2 Materials and Methods
### Metric Analysis  
The signal-to-noise ratio (SNR) is a metric used to evaluate the precision and reproducibility of measurements in impedance imaging. It serves to measure the consistency of repeated measurements conducted under unchanged conditions. The traditional expression for SNR (\(SNR_{i}\)) is formulated by taking the ratio of the mean signal (\(\bar{v}_{i}\)) to the noise level (\(SD[v]_{i}\)) for each measurement channel, as depicted in Equation (1) [34]. \[SNR_{i}=\frac{[\bar{v}]_{i}}{SD_{[v]_{i}}} \tag{1}\]  
In this expression, \(SD_{[\bar{v}]_{i}}\) represents the noise amplitude, determined by the standard deviation of multiple measurements for each channel. Meanwhile, \([\bar{v}]_{i}\) denotes the signal amplitude, estimated through the mean value of multiple measurements for each channel. Calculating the SNR offers valuable information on the reliability and consistency of the measurements, playing a crucial role in ensuring the robustness and accuracy of impedance imaging techniques. Refinement of the evaluation of various objects in EIT at multiple frequencies involves using profile lines that traverse the objects, as shown in Figure 2A. This method improvesthe understanding of how changes in frequency affect the contrast of materials in EIT images. The objectives of employing profile lines include:  
* Evaluating frequency-dependent impedance: These profiles are instrumental in analyzing the impedance characteristics of materials at different frequencies. By intersecting various materials, they reveal impedance changes with frequency alterations. * Quantifying contrast: The data from these profiles are crucial for quantitatively assessing the contrast of different materials. This analysis is key to understanding how EIT images distinguish between materials across the electromagnetic spectrum. * Exploring a range of frequencies: The approach includes a wide spectrum of frequencies to comprehensively study how various materials appear in EIT images at different frequency levels, allowing for a detailed investigation of frequency-related effects. This technique of using profile lines aims to deepen the understanding of EIT imaging, especially for materials with diverse electrical properties, potentially leading to significant advancements in various EIT applications and the study of frequency-dependent contrast in EIT. In evaluating the quality of EIT images, sharpness and contrast parameters play crucial roles [35]. Sharpness, an essential metric for assessing clarity and resolution, is calculated using the gradient method. The formula is given by:  
\[\text{Sharpness}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(\
abla I_{i})^{2}} \tag{2}\]  
In this equation, \(\
abla I_{i}\) represents the gradient of the image intensity at pixel \(i\), and \(N\) is the total number of pixels. The sharpness value provides an average edge contrast across the image, reflecting EIT's ability to accurately delineate boundaries and structures. The contrast parameter is integral in evaluating the system's ability to distinguish between regions of different electrical conductivities [36]. This capability is essential to differentiating between various materials or tissues. Contrast is often calculated based on the intensity values within the image using the following formula. \[\text{Contrast}=\frac{I_{\text{max}}-I_{\text{min}}}{I_{\text{max}}+I_{\text{ min}}} \tag{3}\]  
In Equation (3), \(I_{\text{max}}\) and \(I_{\text{min}}\) represent the maximum and minimum intensity values within the image, respectively. This calculation yields a normalized value, reflecting  
Figure 2: Visualization of assessment metrics with a blue circle (non-conductive object) and a red circle (conductive object): (**A**) profile line; (**B**) contrast-to-noise ratio. the degree of differentiation the EIT system can achieve between the highest and lowest conductivity regions.