H. Bolcskei et al., Design of orthogonal and biorthogonal lapped transforms satisfying perception related constraints, IEEE IM PR, 9(5), 2000, pp. 760-772
We propose a new efficient method for the design of orthogonal and biorthog
onal lapped transforms for image coding applications, It is shown how perce
ption related constraints such as decay and smoothness of the filters' impu
lse responses can be incorporated in the optimization procedure. A decompos
ition of lapped transforms (orthogonal and biorthogonal) with 50% overlap l
eads to an efficient recursive optimization procedure, which is robust with
respect to initial solutions. The importance of this decomposition lies in
the fact that it allows to decouple the design of the even-symmetric and t
he odd-symmetric filters and hence drastically reduces the number of variab
les to be optimized. It furthermore reveals all the variables predetermined
by perception related and coding-efficiency related constraints imposed on
the filters. We present design and coding examples demonstrating the perce
ptual performance and the rate-distortion performance of the resulting tran
sforms.