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.

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.

Restoration of global motion blur requires the blur parameters (direction and extent) to be known. To this end, spectral approaches based on finding zeros in power spectrum or bispectrum estimates are widely reported. In noisy conditions, however, finding spectral zeros is hardly possible as they are covered by the noise power spectrum. In this paper, we separate the determination of blur direction and blur extent. The advantage is that, once the blur direction is known, it suffices to estimate a slice of the power spectrum or bispectrum in this direction. These one-dimensional estimates are considerably less sensitive to noise than higher-dimensional ones. The blur direction is determined by an inertia-like tensor, which assesses spectral anisotropy caused by the motion blur. This approach is applied to noisy low-dose X-ray images, which are particularly hard to process since the blur degrades the signal but not the relatively strong noise.

This contribution describes a new filtering technique for the reduction of noise in medical X-ray images acquired with very low doses, like fluoroscopy images. In such images, only between 10 and 200 X-ray quanta contribute to each pixel. The resulting Poisson statistic causes a strong deterioration of image quality by quantum noise, which, in the observed images, is signal-dependent and exhibits a lowpass-shaped power spectrum. The central part of our approach is a linear/median hybrid filter, which is well-known for its good detail preservation properties. Noise reduction by this filter, however, depends on the presence or absence of underlying signal slopes, and is limited to a small range of spatial frequencies. Also, like median filters this filter tends to generate streaking artifacts. We show how a combination of linear/median hybrid filtering with a multiscale pyramid avoids these shortcomings, while simultaneously improving noise reduction performance substantially.

Describes an algorithm for noise reduction and enhancement of images which is able to take into account anisotropies of signal as well as of noise. Processing is based on subjecting each image to a block DFT, followed by comparing each observed magnitude coefficient to the expected noise standard deviation for it. Depending on this comparison, each coefficient is attenuated the more, the more likely it is that it contains only noise. In addition, the attenuation is made dependent on whether or not the observed coefficient contributes to an oriented prominent structure within the processed image block. Orientation as well as the distinctness with which it occurs are detected in the spectral domain by an inertia-like matrix. Orientation information is additionally exploited to selectively enhance oriented structures, thus only marginally increasing noise as compared to isotropic enhancement.

In a micro-cellular system, radio propagation prediction may be replaced by statistical analysis of the running system, as far as the distribution of the radio resource between cells is concerned. To this end, interference level and channel usage are sampled and correlated. As a result, the estimation of the compatibility of channels being used at different cell sites can be updated and used for a revised channel assignment. This approach may be seen as a special case of the more general idea of self-optimising networks. The feasibility of the method has been studied by simulations.>