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 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.
