Multimedia Signals and Systems by Srdjan Stanković Irena Orović & Ervin Sejdić

Author:Srdjan Stanković, Irena Orović & Ervin Sejdić
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

After expanding the sequence of pixels, the wavelet coefficients are calculated. For the (5,3) integer wavelet transform , the coefficients are calculated according to:

(4.71)

Here, d coefficients represent high frequency components, while s coefficients represent low frequency components.

In the case of the (9,7) floating-point wavelet transform , wavelet coefficients are obtained as follows:

(4.72)

where the constants (wavelet filter coefficients) for the JPEG2000 algorithm are: α = −1.586134342, β = −0.052980118, γ = 0.882911075,

δ = 0.443506852, K = 1.230174105. As in (4.69), d are details, and s are low-frequency coefficients.

Consider a simple example with five consecutive pixels . The (9,7) wavelet coefficients can be calculated in four steps:

The first step is:

The second step is:

The third step is:

The fourth step is:

At the end, d′ coefficients are scaled by the parameter -K and s′ coefficients are scaled by the parameter 1/K. This procedure is illustrated schematically in Fig. 4.30.

Fig. 4.30Calculating the wavelet coefficients

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