A Lapped Directional Transform for Spectral Image Analysis and Its Application to Restoration and Enhancement

We describe a new real-valued lapped transform for 2D-signal and image processing. Lapped transforms are particularly useful in block-based processing, since their overlapping basis functions reduce or prevent block artifacts. Our transform is derived from the modulated lapped transform (MLT), which is a real-valued and separable transform. Like the discrete cosine transform, the MLT does not allow to unambiguously identify spatial orientation from modulus spectra or spectral energy. 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 from spectral energy. Furthermore, a fast and separable algorithm for this transform exists. As an application example, we investigate the transform's performance in anisotropic spectral approaches to image restoration and enhancement, and compare it to the DFT.