  This paper describes a general program for deriving the action of single
field inflation models with nonstandard kinetic energy terms using CMBR power
spectrum data. This method assumes that an action depends on a set of
undetermined functions, each of which is a function of either the inflaton wave
function or its time derivative. The scalar, tensor and non-gaussianity of the
curvature perturbation spectrum are used to derive a set of reconstruction
equations whose solution set can specify up to three of the undetermined
functions. The method is then used to find the undetermined functions in
various types of actions assuming power law type scalar and tensor spectra. In
actions that contain only two unknown functions, the third reconstruction
equation implies a consistency relation between the non-gaussianty, sound speed
and slow roll parameters. In particular we focus on reconstructing a
generalized DBI action with an unknown potential and warp factor. We find that
for realistic scalar and tensor spectra, the reconstructed warp factor and
potential are very similar to the theoretically derived result. Furthermore,
physical consistency of the reconstructed warp factor and potential imposes
strict constraints on the scalar and tensor spectral indices.
