International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
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C LL = (L <g> L)C LL , (L ® L) T 
2 J 1 
C HL = (L ® H)C LL , (L ® tf) 7 
2 ; 2 ; 1 
= (// ® L)C LL , (// ® L) T 
2 J 2 J ~ l 
C HH = (H ® H)C LL , (H ® T/) 7 
2 J 2 J 1 
The reconstruction formulas for the heights according to the 
synthesis equation then read as 
Application of the law of error propagation for the covariance 
matrices yields 
C LL = 
2 ] ~ l 
* * TT* * T 
(L ®L )C ll (L ®L y 
2 J 
* * JJT * * T 
+ (L ®ff )C ML (L ®H y 
2 J 
* * T T-T * * T 
+ (H ®L )C LH (H ®L y 
2 J 
* * jjij * * T 
+ (H ®H )C HH (H ®H y 
2 J 
(4) 
x 
2 j ~ l 
(L ®L)x 2 j +(L ® H*)dx" L + ... 
(H* ®L )dx L £ + (H* ® H*)dx™ 
On the finest level, C^ L is equal to the covariance matrix C. L* 
(3) and H* are the adjoint operators to L and H and deal with the 
inverse transformation. 
100 
300 
200 
Fig. 1. An example of a DTM pyramid based on wavelet transform.