Generalized sampling: a variational approach .II. Applications

For pt.I see ibid., vol.50, no.8, p.1965-76 (2000). The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formulas, which should permit application of the technique directly to problems at hand. We comment on the practical aspects of the method, such as numerical stability and speed. We show the reconstruction formula and apply it to several practical examples, including new variational formulation of derivative sampling, landmark warping, and tomographic reconstruction.