  We consider the inverse source problems with multi-frequency sparse near
field measurements. In contrast to the existing near field operator based on
the integral over the space variable, a multi-frequency near field operator is
introduced based on the integral over the frequency variable. A factorization
of this multi-frequency near field operator is further given and analysed.
Motivated by such a factorization, we introduce a multi-frequency sampling
method to reconstruct the source support. Its theoretical foundation is then
derived from the properties of the factorized operators and a properly chosen
point spread function. Numerical examples are provided to illustrate the
multi-frequency sampling method with sparse near field measurements. Finally we
briefly discuss how to extend the near field case to the far field case.
