The brightness of both images should be matched before fusing. To calibrate the brightness, the intensity component of the other image to be used as reference. The mean and standard deviation of each image can be calculated, these values are used to adjust the brightness of an image to the other reference image. The expression can be written [4] as follow,

I : previous intensity component.
I': calibrated value.
m₁, s₁ reference values of brightness mean and standard deviation, respectively.
m₂, s₂ reference values of mean and standard deviation of image under consideration, respectively.
Both images will be inversely transformed to be the RGB space after adjusting the brightness, then the equation (4) can be rewritten as follows.

The corrected geometrical images after passing the brightness adjust is shown in Fig.1.

(a) JERS-OPS (Feb. 28,1998)



(b)JERS-OPS (Apr. 13,1998)
Fig.1. Corrected geometrical images (a).cloud-covered image (b). cloud-free image
3.Wavelet Decomposition
The wavelet decompositoon is widely used for image processing. The proposed method is based on the image decomposition into multiple-channel depending on their local frequency content. The wavelet transform provides a framework to decompose image into a number of new images, each of them has a different degree of resolution. As the Fourier transform gives an idea of frequency content for image, the wave representation is an intermediate representation between Fourier and spatial representations. It is able to provide the good localization for both frequency and space domains. The wavelet transform of a distribution f(t) can be expressed as follows.

As a and b are scaling and translation parameters, respectively. Each base function ((t-a)/b) is a scaled and translated version of function called other wavelet. These base functions are ò y((t-a)/b)=0.

The discrete approach of the wavelet transform can be done with several different algorithms. To obtain a shift-invariant discrete wavelet decomposition of image. The previous paper [1] proposed to use the wavelet transform algorithm to decompose the image into wavelet planes.

F₁(P) = P₁ ;         F₂(P₁) = P₂ ;         F₃(P₂) = P₃; ...             (8)