## 2 Materials and Methods  
### Storing/Breathing Episodes  
This study was conducted after obtaining approval from the ethics review boards of the Division of Science and Technology, Graduate School of Technology, Industrial and Social Sciences, Tokushima University, and Anan Kyoei Hospital. Sleep sounds were recorded during a PSG test conducted at the Anan Kyoei Hospital. A microphone (Model NT3, RODE, Sydney, Australia) was placed approximately 50 cm away from the patient, and its distance could vary from 40 to 70 cm depending on the patient's movements. Sleep sounds were recorded using a preamplifier (Mobile pre USB, M-Audio, CA, USA), with a sampling rate of 44.1 kHz and digital resolution of 16 bits/sample. However, in this study, the recorded data were downsampled to 11.025 kHz at the time of analysis in consideration of the main SBE components [35; 36].  
The SBEs and non-SBEs used in this study were identified by three annotators who carefully listened to the recorded data. The SBE/non-SBE sections were finally determined from the average values of the start and end points of the SBEs/non-SBE sections identified by the three annotators after they carefully listened to the recordings. The degree of matching of the annotations of the three annotators was calculated using Cohen's kappa [37; 38] to guarantee the reliability of annotations. The SNRs of the SBEs included in the recorded data were calculated from the annotation results using the following equation:  
\[\text{SNR}=10 log_{10}\frac{P_{S}-P_{N}}{P_{N}}, \tag{1}\]  
Herein, \(P_{S}\) and \(P_{N}\) denote the SBE and noise power, respectively. In this study, the recorded data were selected to satisfy the following conditions to evaluate the performance of the proposed method in low-SNR conditions. Furthermore, the recorded data used in this study included a 120 s section extracted from the 6 h sleep sound data, wherein multiple low-intensity SBEs existed which were composed of SBE and non-SBE sections.  
1. The amplitude of SBE within the 120 s interval did not change considerably across all the recorded data
2. SBEs with low SNR were repeated in the 120 s interval of recorded data (1) Exp-1: SBE detection of the recorded data from 25 individuals, wherein as SBEs and non-SBEs only included silence periods and (2) Exp-2: SBE detection of recorded data from 15 individuals, wherein SBEs and non-SBEs included talking, alarm sounds, footsteps, and fan noise which may have occurred during actual sleep. Table 1 shows the subject record databases used in Exp-1 and Exp-2. It can be observed from Table 1 that in Exp-1, the range of average SNR of the SBEs recorded from the OSAS (AHI > 10) and non-OSAS (AHI < 10) subjects ranged from \(-\)8.34 \(\pm\) 1.40 to 0.88 \(\pm\) 3.24. In Exp-2, the range of average SNRs of the SBEs recorded from the OSAS and non-OSAS subjects ranged from \(-\)13.84 \(\pm\) 4.02 to 0.05 \(\pm\) 3.22.  
The average number of segments with SBEs/silence used in Exp-1 was 54.7 \(\pm\) 13.2 and 54.1 \(\pm\) 12.4, respectively. The number of segments with SBEs/non-SBEs used in Exp-2 is described in detail in Table 2. It can be observed from Table 2 that non-SBEs that are expected to occur during actual sleep were used in the experiment.