Sampling theorem and irregular sampling theorem for multiwavelet subspaces

We generalize the multiwavelet sampling theorem by reproducing a kernel that is easy to use. Multiscaling functions that have orthogonality, regularity, short compact support, symmetry, and high approximation order satisfy the conditions in the sampling theorem, which is not possible in the case of the scalar wavelet. We consider the general cases of the uniform noninteger and irregular sampling. A reconstruction from more general sets of points is necessary since the measurements may not be made at uniform points. Finally, we establish a general irregular sampling theorem for multiwavelet subspaces and derive an estimate for the perturbations of uniform noninteger sampling in shift-invariant spaces.