# Speckle Noise Detection and Removal for Laser Speech Measurement Systems
## 2 Related Works  
Restoring audio signals that are corrupted by targeted speckle noise is a tricky process. For information acquisition, any information loss is fatal; thus, for laser speech detection it is imperative to find the location of the speckle noise and remove it in a targeted fashion instead of denoising the whole speech signal. The restoration process can be divided into two steps: detection (finding the locations of the degraded samples) and interpolation (replacing the degraded samples with more suitable values). On the other hand, the noise detection technology can be considered to be a Voice Activity Detection (VAD) [5,6] technology. VAD technology can be divided into frequency-domain methods and time-domain methods. Frequency-domain based methods assume that the energy of the noise is concentrated in the high frequency band, while the energy of the speech is mainly distributed in the low frequency band [7]. However, because laser speech detection focuses on the vibration of an object and there are numerous potential sources of interference, the frequency characteristics of the speckle noise are not completely consistent. Therefore, it is very difficult to distinguish speckle noise and speech using frequency-domain processing. Time-domain methods include energy\(-\)based endpoint detectors [8,9], zero-crossing rate-based methods [10], Autocorrelation Function (ACF) based methods [11] and different  
Figure 3: Raw-detected signal with speckle noise. feature combination detection methods [12; 13; 14; 15]. Energy-based noise detection methods use differences in energy to distinguish noise and speech. However, although the speckle noise energy in laser detected speech is relatively high, in some cases, speckle energy of a very short duration is close to the energy of the speech signal. Therefore, it is impossible to determine an appropriate threshold. Zero crossing rate-based methods represent the number of times a frame of speech signal waveform passes through a horizontal axis. This reflects, in outline, the frequency characteristics of the signal. It is generally thought that a speech segment will have a short-time zero crossing rate that is lower than a certain threshold, while the noise will be higher than the threshold [13]. However, the zero-crossing rate of noise in laser detected speech can be low or high, because the causes of the noise differ. Therefore, it is not possible to set an appropriate threshold to distinguish between speckle noise and speech using a zero-crossing rate. In view of the periodic nature of speech, its ACF is also periodic, with the period being equal to the pitch value. ACF shows peaks at various pitch and harmonics locations. Consequently, ACF-based algorithms are efficient in distinguishing between background noise with a small amplitude and speech. However, they are not so effective for speckle noise. Outside of the above-mentioned, relatively straightforward time-domain and frequency-domain methods, [PERSON] [16] and [PERSON] [17] have developed a kurtosis-based approach for the detection of speckle noise in laser captured signals. As the kurtosis can measure the degree of deviation from a certain distribution [18], it can be applied to identify abnormal speckle samples. Their work introduced a kurtosis ratio (KR)--based method for the detection of speckle noise and the selection of undistorted regions within a signal. Their algorithm is composed of band-pass filtering, signal segmentation and computation of a scalar KR indicator for each signal segment, which can detect outlying samples that are caused by speckle noise. However, this method is not very robust for long\(-\)term speckle samples because the distribution of these impulsive samples becomes similar. Thus, the method is not effective for long-term speckle noise. In speech, speckle noise is represented as impulsive noise in speech.