GENERALIZED IRREGULAR SAMPLING IN SHIFT-INVARIANT SPACES

Abstract

This article concerns the problem of stable recovering of any function in a shift-invariant space from irregular samples of some filtered versions of the function itself. These samples arise as a perturbation of regular samples. The starting point is the generalized regular sampling theory which allows any function f in a shift-invariant space to be recovered from the samples at {rn} n∈ℤ of s filtered versions [Formula: see text] of f, where the number of channels s is greater or equal than the sampling period r. These regular samples can be expressed as the frame coefficients of a function related to f in L 2 (0,1) with respect to certain frame for L 2 (0,1). The irregular samples are also obtained as a perturbation of the aforesaid frame. As a natural consequence, the irregular sampling results arise from the theory of perturbation of frames. The paper concludes by putting the theory to work in some spline examples where Kadec-type results are obtained.