To construct the sequence, this algorithm performs successive convolutions with a filter obtained from auxiliary scaling function. The use of a B₃ cubic spline leads to be a convolution with 5*5 mask.
(9)
The wavelet planes (W1) are computed as the difference between two consecutive approximation p_I-1 and P₁.

As, P₁ are versions of original image P at increasing scales.
W₁ are multi-resolution wavelet planes. 0
P_r is a residual image

4. Methodology and result
Because of continuously and evidently appear in white color of cloud, these attributes will found in both spectral and spatial domains. Otherwise, the shadow of cloud appears in black color. To remove the cloud and its shadow in effectually, the gray level slicing merged as shown in Fig.2.

Fig.2. The clouded image, after passing the gray level slicing process.
The continuity of cloud and its shadow will be separated and removed from the other data with wavelet decomposition techniques as mentioned above and shown in Fig.3. In other to compensate removed data, the low-resolution component of the cloud-free image (P'r) will be added to the residual component of cloud removed image as shown in Fig.4.



Fig 3. The wavelet decomosed image (a), (b) low-frequency and high-frequency term of clouded image (c) low-frequency term of cloud-free image with n=1, and (d),(e) and (f) for n=3, respectively.



Fig. 4. Result form cloud removing after fusing the low and high frequency components.
In Fig.4, the cloud-covered data can be replaced. The low frequency component has no cloud or cloud-free, it can maintain the data which is the high frequency component (P'). these data are needed to keep. To get rid of the cloud edge can be done by applying the image data to the low-pass filter but some data will be lost.

5. Conclusion
The proposed technique in this paper can improve the cloud covered image data. The lost data compensation by fusing with wavelet decomposition, the data may be the same region of area, different time, and different sensor. The collected data depend on the scaling index (n). the selection of scaling index depends on type and quantity of covered cloud. Although, the proposed technique con not compensate all data but this technique is simple and easy to apply.

6. References

• J. Nunez, X. Otazu and R. Ardiol, "Multiresolution-Based Image Fusion with Additive Wavelet Decomposition," IEEE Trans. Geoscience and Remote Sensing, Vol. 37, No. 3, pp. 1204-1211, May 1999.
• Y.C.Liao, T.Y. Wang and W.T. Zheng, "Quality Analysis of synthesized High-Resolutin Multispectral Imagery, " proc. 19yh Asian conference on Remote Sensing, pp. I-1-1 -I-1-6, Nov. 16-19,1998.
• R.C. Gonzaley and R.E. Woods, Digital Image Processing, Addition-Wesley Publishing Company, USA, Sep. 1993.
• F.Cheevasuvit, C. Peanvijarnpong and S. Murai, "Mosaicing of poor contrast images," proc. 9th Asian conference on Remote Sensing, pp. H-1-1-1 - H-1-1-9, Nov. 26-29, 1998.