# Speckle Noise Detection and Removal for Laser Speech Measurement Systems
## 3 Automatic Noise Detection and Removal
### Parameter Setting  
In the proposed automatic noise detection and removal method, the signal is divided into overlapping frames of length \(N\) with a hop size of \(N_{h}\) samples. In practice, we chose \(N_{h}=N/4\), which corresponds to a 75% overlap. If the frames of length \(N\) are greater than the maximum length of the high-energy noise \(N_{max}\), the average energy value will incorporate background noise or speech signals with a smaller amplitude. This results in the threshold rate \(T_{\mathrm{E}}\), being hard to set and the noise being missed or erroneously detected. Simultaneously, if the frames of length \(N\) are too small and they ignore the continuity of an impulse, only the point of the peak will be located, with the middle value of the peaks not being detected. To further complicate matters, in the case of the kurtosis, if the frames of length \(N\) are too short, applying a statistical process will be nonsensical. In terms of delay, overly-long frames of length \(N\) will lead to an excessive time delay.  
In a laser speech measurement system, the duration of speckle noise is variable but generally ranges between 5 ms and 20 ms. Therefore, we set the frame length \(N\) to the largest potential value of 20 ms (i.e., 320 samples at a 16 khz sampling rate) in order to fulfill the requirements for the time delay, and to provide a segment length that is sufficient for reliable estimation of the average energy and kurtosis.  
As for the coding order \(P\), i.e., how many samples are used to predict and replace the contaminated samples, as the predictor order increases for a speech signal, the prediction error decreases. [PERSON] [27] stated that the interpolation error depends on the model order while usually a model order of two to three times the length of missing data sequence achieves good result. [PERSON] [28] suggests using \(P=\){\(3N_{max}+2\)}. However, the algorithmic complexity of calculating the prediction coefficients also needs to be considered with the increase of the coding order. Indeed, it seems fair to assume that \(P\) should be at least greater than \(N_{max}\), so that only known samples are used for the reconstruction [20]. In order to reuse the parameters calculated during the decorrelation preprocessing, \(P\) is set equal to the frame length \(N\), because we previously set the frame length as the maximum length of the speckle noise \(N_{max}\). This is also advantageous since the linear predictor coefficients calculated during the decorrelation stage can be reused in the last step of the coding, which greatly reduces the computation complexity.  
The threshold ratios \(T_{\mathrm{E}}\) and \(T_{\mathrm{k}}\) directly determine the detection accuracy. Several experiments demonstrated that, when \(T_{\mathrm{E}}=5\) and \(T_{\mathrm{k}}=2\), all the speckle noise is visibly removed without any false detection.  
The value averages \(E_{mean}\) and \(K_{mean}\) were dynamically adjusted during the experiments in order to assess what would provide sufficient sensitivity with a minimum number of false alarms. Everyone has to take a break in order to breathe when speaking, and, on average, this occurs every 10 s. Therefore, the average energy value and kurtosis for over 10 s were taken as the basis of these calculations.  
Figure 7 shows the result of locating and replacing the speckle noise in an example of laser measured speech. Figure 7a is the raw noisy signal. Figure 7b shows the noise locations given by the proposed method. The black box shows the noise points located by energy discrimination and the positions marked by an asterisk are the noise points identified by kurtosis. Figure 7c is the speech enhanced by replacing the noise points. For comparison, Figure 7d shows the pure voice.