  One of the interesting problems in the finite-rate-of-innovation signal
sampling framework is the design of compactly supported sampling kernels. In
this paper, we present a generic framework for designing sampling kernels in
2-D. We consider both separable and nonseparable kernels. The design is carried
out in the frequency domain, where a set of alias cancellation conditions are
imposed on the kernel's frequency response. The Paley-Wiener theorem for 2-D
signals is invoked to arrive at admissible kernels with a compact support. As a
specific case, we show that a certain separable extension of the 1-D design
framework results in 2-D sum-of-modulated-spline (SMS) kernels. Similar to
their 1-D counterparts, the 2-D SMS kernels have the attractive feature of
reproducing a class of 2-D polynomial-modulated exponentials of a desired
order. Also, the support of the kernels is independent of the order. The design
framework is generic and also allows one to design nonseparable sampling
kernels. To this end, we demonstrate the design of a nonseparable kernel and
present simulation results.
