A general biorthogonal wavelet based on Karhunen–Loéve transform approximation

Development of computationally efficient biorthogonal wavelets

“…This makes the Daub 5/3 wavelet computationally efficient. The general wavelet proposed by Kale possesses such properties [9].…”

“…Although not having vanishing moments as much as Daub 5/3 wavelet, Kale have proposed a general wavelet as shown in Equation 10which has plausible regularity properties and also provides better decorrelation performances than the Daub 5/3 wavelet on 16 test images [9].…”

“…z/4 and z −1 /16) are simple bitwise shift operations. The wavelet introduced by Kale has shiftings of 4 for prediction (1/4 and z /4) and 9 for update (1/2, 1/16 and z −1 /16) [9] compared to the Daubechies' bitwise shifts of 2 for prediction (i.e.…”

“…Here, there was a problem: The wavelets were signal-dependent. The second research of the author fixed this problem by declaring a general and computationally efficient Kale 5-tap/3-tap (Kale 5/3) wavelet [9].…”

“…The Daub 5/3 wavelet can be realized in the lifting scheme with bitwise additions and shifts and so can the Kale 5/3 wavelet [9,11,20]. This property makes these wavelets computationally efficient.…”