Super-Haar designs of wavelet transforms
Harold H Szu, Joseph P. Garcia, Brian A. Telfer, Raghuveer Rao · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
A linear superposition of Haar transform is given to design an adaptive biorthogonal subband coding. Given Haar scaling function, rect(x), a new symmetric staircase scaling function may be desirable in order to match a specific compression or recognition goal. Then, the associated lowpass filter coefficients are solved from the roots on a unit circle in the z-transform domain. From which the bi-orthogonal and lossless high pass filter is derived for both the forward analysis and the backward synthesis stages. An explicit construction of super-Haar system produces a lossless filter bank which can match an infrared image for achieving pattern recognition and compression simultaneously.