An Orientation-Selective Orthogonal Lapped Transform

A novel critically sampled orientation-selective orthogonal lapped transform called the lapped Hartley transform (LHT) is derived. In a first step, overlapping basis functions are generated by modulating basis functions of a 2-D block Hartley transform by a cosine wave. To achieve invertibility and orthogonality, an iterative filter is applied as prefilter in the analysis and as postfilter in the synthesis operation, respectively. Alternatively, filtering can be restricted to analysis or synthesis, ending up with a biorthogonal transform (LHT-PR, LHT-PO). A statistical analysis based on a 4000-image data base shows that the LHT and LHT-PO have better redundancy removal properties than other block or lapped transforms. Finally, image compression and noise removal examples are given, showing the advantages of the LHT especially in images containing oriented textures.