## 4 Results and Evaluation
### Objective Evaluations  
#### 4.1.1 Evaluation of Noise Reduction Performance  
We will assess the performance of our approach in eliminating background noise by comparing it with two baseline methods. This evaluation involves comparing the noisy audio input to the model with the model's output, which is a denoised signal. The two baseline models are a classical method using Wiener filters and a more recent technique known as Deep Audio Priors Design (DAP). Wiener filters were used by [34] to reduce the noise in audios utilizing the frequency domain. DAP Design is an update of U-Net that uses dilated convolutions and dense connections [35]. The evaluation is made with a set of audios that comprises 400 instances, 100 for each use case. Each audio has a length of 3 s, with a sample rate of 22 kHz and a bid-depth of 16. To make an accurate comparison, we use two metrics: MSE and a Signal-to-Noise Ratio (NSR). The first one measures the Euclidean distance between two images which are the spectrograms of an audio with background noise and the same audio after being processed by the denoising model, [36]. The larger the value of MSE, the greater the difference between the noise signal and the cleaned signal, from which it can be inferred that the model eliminates background noise better. The metric is depicted in Equation (9) where \(y_{i}\) is the value of a particular position in the noisy audio and \(\hat{y}_{i}\) is the value of the denoising audio in the same place. Figure 2: Architecture of the model. \[MSE=\frac{1}{N}\sum_{i=1}^{N}(y_{i}-\hat{y}_{i})^{2} \tag{9}\]  
The second metric measures the difference in decibels (dB) between the same two signals once they have been converted back to the audio domain. SNR values range between \(-35\) and \(35\) dB, which is the theoretical magnitude of noise. The closer the value is to zero (either positive or negative), the better the performance of the model [37]. Equation (10) mathematically formalizes this metric. In the Equation, \(P_{signal\_noise}\) refers to the audio with background noise and \(P_{noise}\) only to the background noise. By subtracting the noise from the noise with the audio, we obtain the audio or signal, allowing us to calculate the signal-to-noise ratio. \[SNR_{dB}=10\log_{10}\biggl{(}\frac{P_{signal\_noise}-P_{noise}}{P_{noise}} \biggr{)} \tag{10}\]  
In Table 3, we compile both metrics and compare our model with the two proposed baselines. It is important to note that MSE is not an accurate metric for assessing audio quality as it does not always align well with the human perception of sound quality that involves subjective factors such as psychoacoustics, human hearing sensitivity, and preferences. When starting with an image that is essentially a Fourier transform of an audio signal, converting it back into an audio signal using the inverse transform does not necessarily reflect how well the audio will turn out. Even a minor change in a single pixel can drastically alter the sound obtained upon reversing the transformation. This fact is due to the use of a parameter of the original audio called the phase of the wave. This parameter is lost when transforming the audio into a spectrogram and a change in its value can make the audio obtained after transforming the spectrogram back into something inaudible. In our case, we have used the Inverse STF, and we have used the phase of the audio with noise that is used as an input in the model. Although the results are not perfect, the evaluation demonstrates that they are good enough, but should be improved in the future. Therefore, MSE values do not precisely represent differences in the quality of the resulting sound. However, we can assert that if the MSE is very low, the two images are highly similar at the pixel level. This implies that the spectrogram obtained after the noise-cleaning process is highly like the original (noisy) one that was fed into the model, meaning that the cleaning process worked poorly.