Lapped directional transform: a new transform for spectral image analysis

We propose a new real-valued lapped transform for 2D-signal and image processing. Lapped transforms are particularly useful in block-based processing, since their intrinsically overlapping basis functions reduce or prevent block artifacts. Our transform is derived from the modulated lapped transform (MLT), which, as a real-valued and separable transform like the discrete cosine transform, does not allow to unambiguously identify oriented structures from modulus spectra. This is in marked contrast to the (complex-valued) discrete Fourier transform (DFT). The new lapped transform is real-valued, and at the same time allows unambiguous detection of spatial orientation. Furthermore, a fast algorithm for this transform exists. As an application example, we investigate the transform's performance in spectral approaches to image restoration and enhancement in comparison to the DFT.