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Empirical mode decomposition (EMD) is a data-driven and multi-scale transform theory, and it is a nonlinear and non-stationary signal processing theory. But each EMD decomposition theory has its advantages and disadvantages. Synthetic aperture radar (SAR) imaging is an important remote sensing technique to obtain the change information, and SAR image data belongs to non-stationary signal. So EMD is very suitable for SAR image processing. There are two kinds of typical EMD theories, which are the ensemble empirical mode decomposition (EEMD) and bidimensional empirical mode decomposition (BEMD). Based on the deep study of the two methods, this paper proposed a new SAR image change detection algorithm, which is called the FCD-EMD algorithm,
*i.e*. fusion change detection based on EMD. So FCD-EMD algorithm can obtain more accurate information, which not only includes the directional information obtained by EEMD, but also can contain the spatial information got by BEMD. The main contribution of the FCD-EMD algorithm is to fuse the detail information in different directions, so that the results obtained are more accurate than the individual method. On the other hand, it can reduce the influence of speckle noise in SAR images by feature selections. The actual SAR image data verify the algorithm proposed in this paper and good experimental results are obtained, which show that the new method is feasible.

Synthetic aperture radar (SAR) imaging has a typical characteristic of obtaining data in all-weather and all-time, so it has been widely used. But SAR is a microwave imaging remote sensing, so the received electromagnetic echo signal is a typical nonlinear and non-stationary signal, and there are some difficulties with traditional methods to process SAR images. Although the wavelet transform and multi-scale geometric analysis theory are very good modern signal processing methods, they are related to the choice of parameters and basic functions in signal processing process. Different parameters and basic functions will bring some influences on the final results. Empirical mode decomposition (EMD) is a kind of completely data-driven and adaptively multi-scale transform theory. It does not need to choose the basic function, but it can adaptively adjust according to the characteristics of the signal itself. Therefore, the EMD theory is better than the wavelet transform and the multi-scale geometric analysis theory; in other words, it can make up for the shortcomings of these typical multi-scale transform theories. EMD can not only deal with linear and stationary signals, but also can deal with nonlinear and non-stationary signals. Especially in non-stationary and nonlinear signal processing, it has great advantages and has been widely used in many fields [

The definition of empirical mode decomposition and the related theory were proposed by Huang in 1998 [

The SAR image is the mapping from the feature space to the image space. SAR receives the electromagnetic echo is scattered from the ground objects, and then after a series of complex processing, then the SAR image is obtained. The echo signal received by SAR is a typical non-stationary and nonlinear signal; meanwhile, the SAR imaging mechanism is the coherent imaging, so the SAR image contains a lot of speckle noise. However, SAR is a microwave imaging which can obtain target area data under all-weather and all-time, and is very suitable for dynamic monitoring and change information acquisition. According to the characteristics of SAR images, after studying the principle of EEMD and BEMD, this paper proposed a new fusion change detection algorithm for SAR images based on different empirical mode decompositions, and it is referred to FCD-EMD algorithm. The feasibility of FCD-EMD algorithm is tested with SAR image data, and good experimental results are obtained.

Using EMD theory to decompose an input signal, we can obtain a finite number of intrinsic mode function (IMF) and a residual quantity. Whether the input signal is linear, nonlinear or stationary, non-stationary, the decomposed IMF features are linear and stationary.

For an input signal x ( n ) , after processing of EMD decomposition, it can be expressed as the sum of the modal characteristic component C i ( n ) and the residua R ( n ) , and definition is given in Equation (1).

x ( n ) = ∑ i = 1 N C i ( n ) + R ( n ) (1)

Here C i ( n ) is the i^{th} IMF component, N is the total number of IMF components.

Although EMD is a fully adaptive data-driven and multi-scale decomposition theory, it is easy to produce the aliasing when there is interference signal in the signal to be decomposed. EEMD adds white noise into the original signal, uses the characteristic that the mean value of white noise is zero, and makes the ensemble average to the IMF feature components obtained by EMD decomposition, which can well eliminate the aliasing. The realization process is as follows.

1) Generate N stripe white noise which is as same as the equal length with the input original signal x ( n ) , the white noise is added into x ( n ) , and the signal which is added by the noise is x i ( n ) .

x i ( n ) = x ( n ) + h i ( n ) , i = 1 , 2 , ⋯ , N (2)

Here x i ( n ) the signal which is added by white noise after the i^{th} time, h i ( n ) is the white noise that is added by the i^{th} time.

2) All x i ( n ) is decomposed by EMD, respectively. Finally, M number of C i j ( n ) and one Residual R i ( n ) is got. Here C i j ( n ) denotes the j^{th} IMF component obtain by adding white noise after the i^{th} time, i = 1 , 2 , ⋯ , N , j = 1 , 2 , ⋯ , M .

3) C i j ( n ) and R i ( n ) perform the ensemble average processing operation, respectively. When N is large enough, the sum of the IMF components which has been added by white noise will tend to zero. The results of the ensemble average are shown as following.

C j ( n ) = 1 N ∑ i = 1 N C i j ( n ) (3)

R ( n ) = 1 N ∑ i = 1 N R i ( n ) (4)

The decomposition process and idea of BEMD is the same as that of EMD decomposition method. A complex two-dimensional signal is decomposed into a number of bidimensional intrinsic mode function (BIMF) components C i B ( m , n ) and a residual R B ( m , n ) by the screening method. Every BIMF component is independent of each other, including the local feature signals of the original signal of different frequencies and different spatial.

Next the two-dimensional image signal is as an example to introduce the screening process of BEMD method. I ( m , n ) denotes the two-dimensional image signal that will be processed, I max ( m , n ) denotes the maximum envelope surface, I min ( m , n ) denotes the minimum envelope surface, and the screening steps are as follows.

1) Finding the local maxima and local minima of the curved surface in an image.

2) Using the interpolation method perform the interpolation operation on the extreme points, and the maximum and minimum envelope surfaces I max ( m , n ) and I min ( m , n ) are obtained.

Computing the mean of the envelope surface I mean ( m , n ) , and I mean ( m , n ) = [ I max ( m , n ) + I min ( m , n ) ] / 2 ; extracting high frequency detail information, i.e. d ( m , n ) = I ( m , n ) − I mean ( m , n ) .

4) Determine whether d ( m , n ) satisfies the two conditions of BIMF. If it does not satisfy, sign I ( m , n ) = d ( m , n ) , repeat steps form step (1) to step (4), until the conditions is satisfied. At this time, d ( m , n ) is a BIMF component, sign C 1 B ( m , n ) , C 1 B ( m , n ) = d ( m , n ) .

5) Sign R 1 B ( m , n ) = I ( m , n ) − C 1 B ( m , n ) , and it is as a new signal to be decomposed, repeat the operations from step (1) to step (4) until the second BIMF component C 2 B ( m , n ) is obtained. Here the residual is R 2 B ( m , n ) = R 1 B ( m , n ) − C 2 B ( m , n ) . Repeat the above steps, until the remainder R i B ( m , n ) has only one extreme point surface, and no longer can any BIMF components be extracted from it.

The image I ( m , n ) can be expressed as a sum of several BIMF components and the residual, i.e. Equation (5).

I ( m , n ) = ∑ i = 1 M C i B ( m , n ) + R B ( m , n ) (5)

Here M is the number of BIMF feature components.

In the step (4) to determine whether the screening process is over, which see if it satisfies the two conditions in the definition of BIMF. The standard deviation (SD) of the two screening results is usually used to determine it. And the definition is given as following.

SD = ∑ i = 0 M [ | d i − 1 ( m , n ) − d i ( m , n ) | 2 d i − 1 2 ( m , n ) ] (6)

Here the value of SD is generally between 0.2 and 0.3, and d i ( m , n ) denotes the i^{th} residual.

When the EMD method is used to process an image, if one wants to extract the much IMF feature information, the original image should have the better direction information. For the SAR images with artificial targets, the direction information is usually obvious. BEMD method is suitable for the processing of SAR images, not only can get abundant BIMF feature information, but also keep the good spatial information of image pixels. Therefore, if the IMF feature and BIMF feature perform the fusion processing, it not only can get more abundant spatial information and direction information, but also is very helpful for target detection and change information obtaining. According to that the SAR imaging mechanism is sensitive to the azimuth; this paper proposes a new SAR image target change detection algorithm based on two different types of EMD decomposition theory, i.e. the FCD-EMD algorithm and its flow chart frame is shown in

1) Input different temporal SAR images, i.e. input SAR images I 1 and I 2 which were obtained from the same target area but at different time t 1 and t 2 .

2) SAR images I 1 and I 2 performs the EEMD decomposition operations in horizontal and vertical direction, respectively.

3) The IMF feature images of horizontal and vertical directions on the same scale are fused to obtain the total IMF feature image for every scale, which are the parts including the frequency information and the detailed information.

4) Select the appropriate IMF feature components. In FCD-EMD algorithm, the first to third scale feature images are selected to perform the next fusion processing operation.

5) The selected IMF feature images are fused to obtain the fused feature images FIMF1 and FIMF2, respectively.

6) The corresponding pixels of feature images of FIMF1 and FIMF2 perform the subtraction operation, and the feature difference image FIMF-D1 will be got.

7) The expectation maximization (EM) algorithm is used to generate an unsupervised detection threshold T 1 in the feature difference image FIMF-D1. EM algorithm is a maximum likelihood estimation method for incomplete data problems, it does not need any external data or prior knowledge, and the detailed implementation process can refer to the document [

8) Obtain the result image D 1 of change detection with EEMD. Using the obtained detection threshold T 1 performs the detection and determination operations in the feature difference image. If D 1 ( m , n ) ≥ T 1 , this shows that the change happens; If D 1 ( m , n ) < T 1 , this shows that there is no changes. Here D 1 ( m , n ) denotes the gray value of the feature difference image at ( m , n ) pixel.

9) Obtain the result image D 2 of change detection with BEMD. The change detection process based on BEMD is similar to EEMD change detection, and it also includes the above several steps. The difference is that BEMD directly decomposes the SAR image, and the two-dimensional feature images BIMF1 and BIMF2 are obtained from the SAR image I 1 and I 2 , respectively. Then the feature selection and fusion processing is performed to generate the feature difference image and the detection threshold; finally, the change detection result D 2 is obtained. After obtaining D 1 and D 2 , they perform the fusion operation, and the change information between SAR images at t 1 and t 2 can be obtained.

10) Fuse the results obtained by the two different methods, and the fusion rule is given by

D ( m , n ) = α × D 1 ( m , n ) + β × D 2 ( m , n ) (7)

Here D ( m , n ) denotes the final result, D ( m , n ) is the result with EEMD and D 2 ( m , n ) is the result with BEMD. The parameters α and β are their weight value, respectively, and the value ranges of them is [ 0 , 1 ] , and here α = β = 0.5 .

In order to verify the feasibility of the proposed algorithm, the simulation experiments and the verification test of measured data are carried out. The experimental SAR image data came from the Sandia National Laboratories [

focus on the acquisition of direction information and geometric detail information; BIMF features in BEMD focus on the acquisition of the spatial information of the target (the correlation of neighboring regions). Through the fusion, the formation of complementary advantages, one can get a better change detection effect, which is shown in

The SAR images in

The results of change detection in

Empirical mode decomposition is a fully adaptive data-driven signal processing theory. Although there are many kinds of decomposition methods, each method has its advantages and disadvantages. EEMD can obtain very good directional information, and BEMD can get the spatial information of the pixel. The proposed FCD-EMD algorithm fuses their advantages, holding good directional and spatial characteristics; at the same time, the new method can reduce the influence of speckle noise on obtaining change information with multi-temporal SAR images. So more accurate information will be obtained by the FCD-EMD algorithm that that of the single EMD method. The experimental results of simulation experiments and the measured SAR images show that the FCD-EMD algorithm can obtain good effects. This shows that the new proposed algorithm is feasible. In the future work, we will make a deep study of the quantitative analysis of the method.

The work was supported by Natural Science Foundation of China (No. 61379031, 41574008), Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JM6052) and Special Foundation for Special Talents of Xijing University (No. XJ17T04).

Huang, S.Q., Liu, Z.G., Liu, Z. and Wang, L.P. (2017) SAR Image Change Detection Algorithm Based on Different Empirical Mode Decomposition. Journal of Computer and Communications, 5, 9-20. https://doi.org/10.4236/jcc.2017.58002