Non-Bandlimited Resampling of Images

The resampling of discrete-time signals where the underlying analog signal is non-bandlimited is considered in this paper. We extend the generalized sampling theory developed based on the principle of consistency to resampling. Realizing the resampling system has both discrete input and output, the performance of the resampling filter is considered in l² instead of the traditionally used L² . We show that the performance of the resampling system depends on the resampling rate instead of the actual interpolating kernels. The theory can be applied to image processing applications like zooming to provide better response to high frequency components. Since the resampling process is discrete in nature, our filter designed to optimize resampling in l² is shown to outperform other techniques designed in L²