Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection

A discrete 2D p:q lattice is comprised of known pixel values spaced at regular p:q intervals, where p, q are relatively prime integers. The lattice has zero values elsewhere. Sets of new symmetric convolution masks were constructed recently whose purpose is to interpolate values for all locations around each lattice point. These symmetric masks were found to outperform the traditional asymmetric masks that interpolate in proportion to the area each pixel shares within a p:q neighbourhood. The 1D projection of these new 2D symmetric masks can also be used when reconstructing images via filtered back-projection (FBP). Here the 1D symmetric filters are shown to outperform the traditional Haar filters that are built from the area-based masks. Images reconstructed using FBP with symmetric filters have errors up to 10% smaller than with Haar filters, and prove to be more robust under Poisson noise.