Mladen Tomic

Denoising one-dimensional signals by wavelet shrinkage critically depends on the choice of wavelet basis, yet basis selection is often guided by heuristics rather than explicit statistical criteria. This paper investigates the relationship between wavelet-basis properties and the shape of the probability density function (PDF) of the detail coefficients in the coarsest retained detail subband. On this basis, it proposes the shape of this PDF as a criterion for wavelet-basis selection. We hypothesize that, for a fixed decomposition depth, noise model, and shrinkage rule, a basis better matched to the signal’s local regularity produces a narrower and more sharply peaked coefficient PDF in this subband than a mismatched basis and can therefore serve as a data-driven indicator for basis selection. To evaluate the consistency of this proposal, we perform controlled hard-thresholding experiments on six canonical test signals, five wavelet bases, and additive white Gaussian noise. Although the test signals differ significantly in local regularity and features, the relationship between basis suitability and PDF shape is confirmed for each of them. Therefore, the results suggest that the proposed PDF-shape criterion is a valuable indicator for wavelet-basis selection.

Usage of cloud systems for data storage has many advantages over the traditional approaches. It is already widely used and its popularity is still fast-growing. The systems must be implemented and maintained in a way that not only satisfies the performance and resource availability requirements, but also fully addresses the questions of security, privacy and data ownership. However, concerns related to those questions very often lead to considerations of a private cloud implementation. In this paper, we explore a private cloud implementation suitable for small to medium businesses. We introduce main types of cloud computing as basic service models and analyze private cloud systems features. Advantages and disadvantages in comparison to public cloud services are considered. Implementation of private cloud solutions in a lab environment allowed us to examine the ease of the setup and maintenance as well as the usability of the chosen solutions and their applicability for the target user group.

Wavelet transforms found widespread application in signal denoising. Many adaptive algorithms were proposed to improve their performance, especially about edges in a signal. In this study, the authors propose a novel denoising method based on adaptive edge-preserving lifting scheme – intersection of confidence intervals-edge preserving lifting scheme (ICI-EPL). By incorporating the statistical method of intersection of confidence intervals rule into the lifting scheme, the authors are able to select the most appropriate wavelet on a point-by-point basis. The resulting transform adapts very well to local signal properties and significantly improves denoising performance. Simulations on various signal classes show that the ICI-EPL in most cases easily outperforms other considered transforms, with the greatest improvement being about edges in a signal. Achieved results bring confidence that the ICI-EPL can be used to improve performance in a variety of denoising applications.

An adaptive lifting scheme is proposed, in which the intersection of confidence intervals (ICI) rule is used to determine the wavelet support. The adaptation is performed on a point-by-point basis and the ICI rule is used to prevent the support from spanning across the edges in a signal, in which the edge is considered to be any sudden change in the signal statistics. It is shown that the proposed method preserves the edges well, and the overall denoising performance is much better than in the other considered methods.