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2010 3rd International Congress on Image and Signal Processing (CISP2010)

An EMD-based Denoising Method for Lidar Signal YiKun Zhang, XiaoChang Ma, DengXin Hua, YingAn Cui, LianSheng Sui

Xi'an University of Technology Xi'an, China E-mail:ykzhang163@163.com

Abstract—Lidar echo signal is a typical non-steady-state, non-stationary signal, and difficult to be dealt with by the traditional filtering methods. As a new signal processing theory proposed in recent years, Empirical Mode Decomposition method can adaptively divide the lidar echo signal into different intrinsic mode function (IMF) components according to different time scale, and noise mainly concentrates in the high-frequency component. However, when filtered with simply removing high frequency component, the useful signal will be possible to be reduced. In this paper, a new method which combines Empirical Mode Decomposition (EMD) with Savitzky-Golay filter is proposed. With experiments, it is indicated that our approach not only removes the noise component effectively but also maintains the useful signal, then will improve the accuracy in the next phase of data processing.

Keywords-Lidar; Denoising; Empirical mode decomposition; Savitzky-Golay

I. INTRODUCTION Usually, the signal is interfered with a variety of noise

during signal detection and transmission at different levels. Particularly, the lidar signal is seriously contaminated for two reasons. One is that the signal is weak in itself; another is that the signal is easily affected by some factors such as the ray radiation from the sun and sky, the dark current noise and thermal noise from the optical detection system. In order to improve the retrieval accuracy of data for the next work, de-noising operation is an indispensable key step. Most of traditional signal processing methods are based on Fourier transform and Wavelet transform. However, the lidar signal is a typical non-linear, non-stationary signal, and the Fourier transform isn’t suitable for it. In addition, the basis function is difficult to determine for wavelet analysis [1]. In 1998, N. E. Huang [2] proposed a new signal processing method, referred as Hilbert-Huang Transform (HHT). The HHT method decomposes the real fluctuations or trends in the different scales sequentially with Empirical Mode Decomposition (EMD) method, and then generates a series of data sequence with different characteristic scales. Each sequence is called as an intrinsic mode function (IMF) and IMF component have good properties from Hilbert transformation. The instantaneous frequency calculated by the Hilbert transformation is characterized as the frequency content in the original signal. This method avoids the insufficient that the Fourier Transformation needs many harmonic components to express the non-linear, non-stationary signals.

Currently, the EMD method has become a hot topic in the lidar signal processing fields [3-8]. This method can filter and extract the trend term from the original signal. When the signal is mixed with random noise, the noise is often found in high

frequency IMF components. In order to get the original signal, these high-frequency IMF components need to be removed. But the effective signal will be also filtered, and the integrity of original signal will be undermined. According to this problem, this paper proposed a new de-noising method based on EMD. With the premise of ensuring the integrity of the signal, this approach will improve the signal noise ratio of the signal.

II. EMD METHOD The EMD decomposition method is based on the following

assumptions: (1) The signal has at least two extreme values, namely a maximum and a minimum; (2) The characteristic time scale is defined as the time interval between extremes; (3) If the signal has no extreme points, but has inflection points, then the extreme values can be computed through one or more differentials. The detailed algorithm can be described as follows [1]:

a) Determining all the local extreme points of the signal, the upper and lower envelopes are formed by interpolating these points with the cubic spline curve.

b) Denoting the mean value of upper and lower envelope as 1m , and with the following equation the quantity 1h will be computed.

1 1( )x t m h− = (1)

If 1h is an IMF, then h1 is the first IMF component of ( )x t .

c) If 1h does not satisfy conditions for IMF, then will be input as the signal data. Repeating steps a) - c), the new mean value of upper and lower envelope, marked as 11m , will be obtained, and then 11 1 11h h m= − will be computed and evaluated whether satisfies IMF conditions. If not satisfied, the above steps will be repeated k times, and finally 1kh is obtained to satisfy IMF conditions. Denoted with 1 1kc h= ,

1c will be the first component of the signal ( )x t .

d) Separating 1c from ( )x t , the 1r will be input as original data and computed with the following equation

1 1( )r x t c= − (2)

Repeating steps a) - d), the second component of ( )x t that satisfies the IMF conditions, denoted with 2c , will be obtained.

e) Repeating the above steps n times, the n components of ( )x t will be computed. Then the signal can be denoted with the following formulation

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1( ) ( ) ( )

n

j nj

X t c t r t=

= +∑ (3)

The term nr denotes the residue and represents the overall trend of the signal.

Because the noise is concentrated in the high frequency components of signal that are the first few IMF components, one can firstly get rid of noisy high-frequency components and then reconstruct the remaining components to get the de-noised signal. However, this method is defective. During the decomposition, the components are forced to be zero-line symmetric, namely the signal is decomposed adaptively. So the first few components of EMD decomposition differ from the detailed components of wavelet transformation, and cannot be removed blindly. When some IMF components are completely filtered out, which is mandatory noise reduction, although the noise is removed, the integrity of the signal is also undermined. Because some useful data of the signal are filtered, the subsequent analysis and processing accuracy of the signal will be affected. According to the above problem on the EMD method, this paper proposes a method which combines Savitzky-Golay filter [9] with the EMD, not only ensuring the signal integrity but also improving the signal to noise ratio of signal effectively.

III. DENOISING METHOD BASED ON EMD From the point of signal processing view, EMD

decomposition is a process which continuously filters high-frequency components into low-frequency components and reflects the multi-resolution of the filtering process. With EMD method, a limited number of sub-intrinsic mode functions are obtained. Because the feature scale parameters defined as the time interval between the extreme points are computed with the measured data, the sub-IMF obtained by the screening of the data according to the characteristic scale parameters usually has obvious physical meaning. Each IMF represents the modal with special feature scale parameters. The signal is screened from the smallest characteristic, and obtained the intrinsic mode function of the shortest cycle. In this way, more IMFs are obtained with increasing cycle lengths. This process reflects the multi-resolution analysis of the filtering. Short cycle means the high frequency components of IMF that contain noise and some effective signal. If these components are completely removed, it will cause signal loss. Therefore, how to extract the effective signal is a key step of improving the accuracy of the signal processing.

The principle of Savitzky-Golay filter algorithm can be described in this way. Firstly, a polynomial is fit with the points in the neighborhood window of ix that the size of window is set to n. The value of ix is substituted with the smooth value ig computed by the polynomial with the following equation

0

Mi

i kk

x xg b k

x=

−=

Δ∑ (4)

In above equation, M is the order of the polynomial; kb is coefficients of the polynomial that need to be computed.

Secondly, smoothing will be implemented by sliding the window along every point [9]. This operation can effectively remove the spikes of the raw data, and make sure that the filtered data only excludes the interference signal and retains the main features of the signal. The main purpose of further processing high-frequency components is to retain the main features of the signal, and to filter out interference and noise. So, the Savitzky-Golay filtering algorithm can be perfectly used to process the high frequency components of IMF.

Accordingly, the paper proposes a new method which combines EMD method with the Savitzky-Golay de-noising method, referred to as EMD-Golay algorithm. The basic principle of our approach can be described in the following steps. Firstly, the original signal is broken into IMF components with high frequency and low frequency bands according to different characteristic scales by using the EMD method. The noise is mainly concentrated in high-frequency components of IMF. Secondly, the first few high-frequency components for further processing are chosen. In this paper, the number of the chosen components is N/2. Then, the selected IMFs are smoothed by using the Savitzky-Golay algorithm, and the main features of high frequency components are obtained. Finally, the filtered signal can be reconstructed with these features of the high frequency and the remaining untreated component.

IV. EXPERIMENTAL AND ANALYSIS

Figure 1. Lidar echo signal

The intensity of lidar echo signal is inversely proportional to the distance, which means the farther the distance is and the weaker the intensity is. In order to obtain better vision effects and easier analysis, we only take a section of the signal to analyze. The measured data is shown in Fig. 1. After the decomposition with EMD method, the IMF and the remaining components are shown in Fig. 2.

From Fig.1 and Fig.2, it can be seen that four IMF components and a remainder are obtained from the original signal by using the EMD method. Among them, the noise is mainly concentrated in the high frequency IMF1. In order to verify our approach, the Savitzky-Golay filter is used to filter IMF1.

After several comparative experiments, we found that the best filtering results could be achieved when cubic polynomial was fit in the window that the size was 5. The effects before and after filtering are shown in Fig.3. From this figure, it is

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obvious that the final results are smoother than ever before and maintains the volatility trends and main characteristics of the signal.

Figure 2. EMD method decomposition

Figure 3. Contrast between the original signal and processed signal of IMF1

Finally, the original signal is processed in two ways by using our approach (EMD-Golay) and the method that removes high frequency components (IMF1) directly. The

results are shown in Fig.4 and the evaluating performances are shown in table 1. Obviously, it is indicated that our EMD-Golay de-noising algorithm can maintain more useful components of the original received signal, and make the final result much smoother because it is more effective that the noise is removed.

Figure 4. The effect graphs between EMD filtering method and EMD-Golay

algorithm

TABLE I. THE RESULT OF TWO METHORDS

Methods SNR Standard Deviation EMD 19.7957 0.0807 EMD-Golay 22.9563 0.0797

V. CONCLUSION In this paper, our EMD-Golay de-noising algorithm based

on the EMD method and the further processing by Savitzky-Golay filtering method for the high-frequency IMF components can reduce the noise effectively. In addition, experimental results show that the principle of the proposed algorithm is simple. Our approach is easy to be implemented, and avoids the complex calculation process needed in other methods such as the wavelet transformation method.

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