Data fusion using 2d discrete wavelet transform (DWT)
If I remember my wavelet transform correctly, this is what happens. Let's imagine that we are working with only the LOW image at the moment. I perform the first-scale decomposition which gives me the LOW_A0 (approximation) and the three detail coefficient images which are LOW_H0, LOW_V0 and LOW_D0. Then, to perform the second scale decomposition, you take the approximation image LOW_A0 and obtain LOW_A0_A1 (approximation) and the corresponding three detail coefficient images LOW_A0_H1, LOW_A0_V1 and LOW_A0_D1. Finally, in the last scale decomposition, you will split LOW_A0_A1 into its corresponding approximation coefficients LOW_A0_A1_A2 and the final detail coefficient images LOW_A0_A1_H2, LOW_A0_A1_V2 and LOW_A0_A1_D2.

So at the end you are left with the following:
1) The lowest approximation coefficients LOW_A0_A1_A2
2) The detail coefficients at each level which are 9 in number (LOW_H0, LOW_V0, LOW_D0, LOW_A0_H1, LOW_A0_V1, LOW_A0_D1, LOW_A0_A1_H2, LOW_A0_A1_V2 and LOW_A0_A1_D2).

Now, also consider that in parallel you have also performed the wavelet decomposition for the HIGH image and you have the same end stage products which are:
1) The lowest approximation coefficients HIGH_A0_A1_A2
2) The detail coefficients at each level which are 9 in number (HIGH_H0, HIGH_V0, HIGH_D0, HIGH_A0_H1, HIGH_A0_V1, HIGH_A0_D1, HIGH_A0_A1_H2, HIGH_A0_A1_V2 and HIGH_A0_A1_D2).

You want to now reconstruct a FUSED image which contains information from both the LOW and the HIGH images. At this stage, you would apply the fusion algorithm. Average the lowest approximation coefficients k*LOW_A0_A1_A2 + (1-k)*HIGH_A0_A1_A2, where k= 0.5 for equal weighting (you may want to weight one more than the other). Then, sum the detail coefficients at each of the corresponding LOW and HIGH detail coefficients. For example, 
LOW_H0 + HIGH_H0.

Now take these approximation coefficient and detail coefficients and do the wavelet synthesis to get the final result. Does this make sense? I haven't read the paper/thesis you pointed out to though.