O-MOMS Supersampling routine

Supersampling function using Optimal Maximal-Order-Minimal-Support as kernel.

MOMS (maximal-order-minimal-support) functions give the least number of supports for a given approximation order L. The stringent requirement of number of supports is critical to real-time signal processing, which is why sinc (the kernel that gives ideal reconstruction) is not used in practice. B-spline based interpolating kernels are usually used in spline interpolation. MOMS functions are constructed by b-spline functions. Here we provide an implementation of O-MOMS (optimal MOMS), which outperforms b-spline kernels of the same degree.

This implementation uses DTFT to compute the coefficients in the prefiltering step [Thevenaz 2000]. For boundary condition, we assume periodic, which is scheduled to be changed to mirroring in the next release.

Degrees of 0 through 5 are supported.

Related papers:

T. Blu et al.

Minimal Support Interpolators with Optimum Approximation Properties, ICIP 1998;
MOMS: Maximal-Order Interpolation of Minimal Support, IEEE Transactions on Image Processing Vol. 10, No.7, 2001;

Phillippe Thevenaz et al.
Interpolation Revisited, IEEE Transactions on Medical Imaging, Vol. 19, No. 7, 2000.