The choice of B-spline biorthogonal wavelets for image coding according to time-frequency resolution

This paper concisely analyzes the influence of the choice of wavelet bases on coding efficiency and quality when image and video coding are based on the wavelet transform. From the point of view suitable for extracting high frequency components of image and video signals, the paper presents the standard of the choice of B-spline biorthogonal wavelets according to time-frequency resolution property, also gives the construction process of B-spline biorthogonal wavelets. A method is proposed in the paper, which can be used for calculating the area of time-frequency window. Moreover, as for every B-spline function with N order (2≤N≤20), the condition of its decomposition wavelet with optimum time-frequency resolution property is given, which suggests that the lower the order of B-spline function is, the better the time-frequency resolution property of its decomposition wavelet is, and that the time-frequency resolution property of B-spline biorthogonal wavelets with even orders is comparatively superior to that of B-spline biorthogonal wavelets with odd orders. On this condition, corresponding dual scaling function and wavelet can be obtained.