Two-channel sampling in wavelet subspaces

We develop two-channel sampling theory in the wavelet subspace V1 from the multi resolution analysis {Vj}j∈𝕫. Extending earlier results by G. G. Walter [11], W. Chen and S. Itoh [2] and Y. M. Hong et al [5] on the sampling theory in the wavelet or shift invariant spaces, we find a necessary and sufficient condition for two-channel sampling expansion formula to hold in V1.

Sampling Theorems of Wavelet Subspaces with M Band in Higher Dimensions

Sampling theorem has a key role in signal processing and image processing. In this paper, the scaling functions with cardinal property are discussed in the dimensions and their symmetry property is classified. Therefore, sampling theorems of wavelet subspaces are obtained. Then, the cardinal orthogonal scaling function with cardinal property is characterized in the dimensions and an equation between the highpass filter coefficients and wavelet samples are got. The existing results are generalized to the case of M band.