Error estimates for nonuniform sampling

Kaczmarz Iterative Projection and Nonuniform Sampling with Complexity Estimates.

Kaczmarz's alternating projection method has been widely used for solving mostly over-determined linear system of equations A x = b in various fields of engineering, medical imaging, and computational science. Because of its simple iterative nature with light computation, this method was successfully applied in computerized tomography. Since tomography generates a matrix A with highly coherent ...

Nonuniform Sampling and Multiscale Computation

We consider multiscale functions of the type that are studied in averaging and homogenization theory and in multiscale modeling. Typical examples are two-scale functions f(x, x/ ), (0 < << 1) that are periodic in the second variable. We prove that under certain band limiting conditions these multiscale functions can be uniquely and stably recovered from non-uniform samples of optimal rate. The ...

Spectral Estimation Using Nonuniform Sampling

Nonuniform data appears in many applications including phased array radar. If a radar is tracking several targets, it may pulse each target at nonuniformly spaced instants in time. One may characterize a target's motion by its precession and spin frequencies, which can be determined from the radar return. Several methods for spectral estimation using nonuniform sampling are presented and compar...

\nonuniform Sampling: Bandwidth and Aliasing"

For spectroscopic measurements there are good reasons why one might consider using nonuniformly nonsimultaneously sampled complex data. The primary one is that the e ective bandwidth, the largest spectral window free of aliases, can be much wider than with uniformly sampled data. In this paper we discuss nonuniformly nonsimultaneously sampled data, describe how these data are traditionally anal...

Nonuniform Sampling : Bandwidth and Aliasing