This paper studies the image fusion of highresolution panchromatic image and lowresolution multispectral image. Based on the classic fusion algorithms on remote sensing image fusion, the PCA (principal component analysis) transform, and discrete wavelet transform, we carry out indepth research. The compressed sensing (CS) abandons the full sample and shifts the sampling of the signal to sampling information that greatly reduces the potential consumption of traditional signal acquisition and processing. We combine compressed sensing with satellite remote sensing image fusion algorithm and propose an innovative fusion algorithm (CSFWTPCA), in which the symmetric fractional Bspline wavelet acts as the sparse base. In the algorithm we use Hama Da matrix as the measurement matrix and SAMP as the reconstruction algorithm and adopt an improved fusion rule based on the local variance. The simulation results show that the CSFWTPCA fusion algorithm achieves better fusion effect than the traditional fusion method.
Numerous interference factors are always mixed in the process of image acquisition and transmission. The images we get are mostly random. PCA [
Olshausen and Field [
We combine compressed sensing theory into PCA and propose a kind of fusion method based on CSFWTPCA algorithm. We apply the proposed algorithm, the traditional PCA transform, and some improved PCA transform, respectively, in image fusion. Simulation results show that the fusion image based on CSFWTPCA has good spatial resolution and also efficiently keeps the spectrum feature of the original multispectral image.
Candes and Tao [
The traditional linear measurement model written in matrix form is as follows:
Putting (
Thus, the optimization problem in formula (
In conclusion, the implementation of compressed sensing theory includes three basic elements: signals’ sparse expression, noncorrelated observation of the measurement matrix, and nonlinear optimization reconstruction of signals. Signal sparsity is the necessary condition for CS theory, measurement matrix is the key, and nonlinear optimization is an approach of CS theory to reconstruct signal [
Compressed sensing theory framework.
The differences between CS theory and traditional sampling theorem [
Firstly, traditional sampling theorem takes the infinitelength continuous signal into consideration, but CS theory concerns the vector of finite dimension.
Secondly, traditional sampling theorem obtains data by uniform sampling; by contrast, CS theory gets observed data by utilizing the inner product of signal and measurement function.
Lastly, the difference between signal reconstructions is as follows. Traditional sampling recovery uses linear interpolation of SINC function to obtain signal, but CS theory turns to solve highly nonlinear optimization problem from the current observed data to get signal.
We apply compressed sensing theory which is combined with PCA to satellite remote sensing image fusion and choose fractional
In 1999 for the first time Unser and Blu popularized spline function to fractional order on the basis of polynomial splines by fractional
Fractional
This paper presents an improved fusion rule: registering images before PCA transform to the MS image. Then, we select the
The flow chart of the satellite remote sensing image fusion algorithm based on compressed sensing, PCA transform, and fractional
Satellite remote sensing image fusion method based on the CSFWTPCA.
The concrete steps are as follows.
The correlation coefficient of two sets of lowfrequency subpictures
Determine the size of a local region
First, the local deviation is defined as
Second, the matching matrix is expressed as
Set the threshold of matching degree
If
We simulate the proposed algorithm by using MATLAB 7.8. Two groups of experimental data are adopted: one is the LandsatTM (MS image, resolution ratio is 30 m,
Group one: (a) LandsatTM image (30 m,
When taking the
The fusion parameters change curve corresponding to the different numbers of wavelet order. (a) EN, AG, CC, and DE of fusion image of LandsatTM and SPOT. (b) EN, AG, CC, and DE of fusion image of IKONOS.
In Figure
Four different methods are adopted, respectively, to fuse satellite remote sensing images, including traditional PCA transformation [
Fusion image of LandsatTM and SPOT. (a) PCA; (b) DWT; (c) FWTPCA; (d) CSFWTPCA.
Fusion image of IKONOS. (a) PCA; (b) DWT; (c) FWTPCA; (d) CSFWTPCA.
Comparing the relevant images in Figures
In this paragraph, the objective evaluation method will be used to analyse the information entropy, average gradient correlation coefficient, and torsion resistance of fusion images for each fusion method. Tables
LandsatTM and SPOT image data fusion performance evaluation 1.
EN  AG  

R  G  B  R  G  B  
PAN  7.4075  7.4075  7.4075  13.1554  13.1554  13.1554 
MS  7.4638  7.4244  7.4122  6.6873  6.485  6.6413 
PCA  7.4942  7.5570  7.4307  10.8695  10.6396  10.7393 
DWT  7.5512  7.5345  7.5034  11.1628  11.0917  11.3812 
FWTPCA  7.6187  7.7086  7.5206  13.2971  13.1768  13.2113 
CSFWTPCA 






LandsatTM and SPOT image data fusion performance evaluation 2.
CC  DE  

R  G  B  R  G  B  
PAN  0.7091  0.6961  0.6128  32.2877  27.6492  28.5331 
MS  0.7091  0.6961  0.6128  0  0  0 
PCA  0.7176  0.6830  0.6556  27.5283  27.1905  27.5072 
DWT  0.8403  0.7926  0.7849  16.9660  27.6493  28.5331 
FWTPCA  0.8874  0.8618  0.7301  16.7670  16.5377  16.6828 
CSFWTPCA 






IKONOS image data fusion performance evaluation 1.
EN  AG  

R  G  B  R  G  B  
PAN  7.7376  7.7376  7.7376  29.6375  29.6375  29.6375 
MS  7.8316  7.6849  7.6202  12.2342  12.0416  11.5112 
PCA  7.8468  7.7716  7.7817  24.5896  22.3556  22.0533 
DWT  7.8592  7.7098  7.7089  27.4281  27.6365  27.5637 
FWTPCA  7.8723  7.7476  7.7722  29.4191  29.6374  29.6375 
CSFWTPCA 






IKONOS image data fusion performance evaluation 2.
CC  DE  

R  G  B  R  G  B  
PAN  0.7847  0.7846  0.7822  28.9117  27.3725  43.107 
MS  0.7847  0.7846  0.7822  0  0  0 
PCA  0.8086  0.8058  0.7954  31.3666  30.8954  31.0786 
DWT  0.8391  0.8279  0.8326  29.1504  28.8737  29.7480 
FWTPCA  0.8654  0.8519  0.8063  25.5072  27.3725  26.1070 
CSFWTPCA 






From the data in Tables
In Tables
These parameters show that after the traditional PCA transform, the information entropy is minimum, the average gradient and torsion resistance are comparatively large, the correlation coefficient is minimum, and the fusion effectiveness is worse than other methods. The reason of this is that in PCA transformation, the first principle component represents the image that changes most and the image of the first principle component has more spatial details. So it has more similar correlation with panchromatic image; the fusion image obtained by this method remains more spectral information and has better comprehensive effectiveness.
With great approximation capability, symmetry fractional
In this paper, we introduced the compressed sensing and its application and then described the image fusion algorithm based on CSFWTPCA. In the simulation that followed, two groups of experimental data are fused separately by using the proposed algorithm, the classical PCA fusion method, the wavelet transform, and FWTPCA fusion rules. A conclusion can be drawn that the FWTPCA and CSFWTPCA algorithms are obviously superior to others, and the effect of the CSFWTPCA algorithm is optimal. But the compressed sensingbased algorithm requires too much time in simulation. Our next job can be focused on improving the image fusion efficiency of the proposed algorithm and reducing the simulation time.