Spectral Extrapolation With Spatial Constraints

A new technique is described for improving transform encoded signal reconstruction by extrapolating missing coefficients in the transform domain. The extrapolation algorithm is very simple and it can easily be incorporated into one-and two-dimensional transform hardware. Examples of signal reconstruction are included for one- and two-dimensional signals. The extrapolation algorithm is especially simple in the case of the Haar transform, due to the global-local properties of the Haar coefficients. The generalized formula is derived for both Haar and Walsh-Hadamard transforms. The incorporation of the spectral extrapolation into a real time bandwidth compression system is also described.