Abstract: It is well known that a bandlimited function can be
reconstructed in theory from a discrete set of its Fourier samples, provided
that the samples are dense enough. This fact is a direct consequence of
extensive studies on Fourier frames for However,
when the sample points do not form a lattice, there is no practical scheme (to
our knowledge) for the reconstruction of f.
In this paper, we propose a fast and easy to implement technique, for
reconstructing a compactly supported function f from finitely irregular samples of The scheme
is based on the cubic-spline interploation and Gaussian spectral mollifiers. The
scheme allows us to eliminate the Gibbs oscillations in many cases.
Keywords and phrases: frames, tight frame, discrete singular convolution.
