Discrete-Time fractional Brownian motion (DFBM) and its increment process, called discrete-time fractional Gaussian noise (DFGN), are usually used to describe natural and biomedical phenomena. These two processes are dominated by one parameter, called the Hurst exponent, which needs to be estimated in order to capture the characteristics of physical signals. In the previous work, a variance estimator for estimating the Hurst exponent directly via DFBM was provided, and it didn't consider point selection for linear regression. Since physical signals often appear to be DFGN-type, not DFBM-type, it is imperative to first transform DFGN into DFBM in real applications. In this paper, we show that the variance estimator possesses another form, which can be estimated directly via the autocorrelation functions of DFGN. The above extra procedure of transforming DFGN into DFBM can thus be avoided. On the other hand, the point selection for linear regression is also considered. Experimental results show that 4-point linear regression is almost optimal in most cases. Therefore, our proposed variance estimator is more efficient and accurate than the original one mentioned above. Besides, it is also superior to AR and MA methods in speed and accuracy.

Burst assembly at edge nodes is an important issue for the Optical Burst Switching (OBS) networks because it has a great impact on the traffic characteristics. We analyze the assembled traffic of the Science Information Network (SINET) by using the Fractional Brownian Motion (FBM) model. The analytical and simulation results show that existing assembly schemes cannot avoid increasing the burstiness, which will deteriorate the network performance. Here, burstiness is defined as the variance of the bitrate in small timescales. Therefore, we address the issue of how to reduce the burstiness of the assembled network traffic. Firstly, a sliding window-based assembly algorithm is introduced to reduce the burstiness of assembled traffic by transmitting bursts at an average rate in a small timescale. Next, an advanced timer-based assembly algorithm is introduced, by which the traffic rate is smoothed out by restricting the burst length to a threshold. The simulation results show that both the sliding window-based and advanced timer-based assembly algorithms perform better than existing assembly algorithms do in terms of the burst loss ratio. The simulation also indicates that the advanced timer-based assembly algorithm performs better in terms of the edge buffering delay than the sliding window-based assembly algorithm does.

Numerous studies have shown that scaling exponents of internet traffic change over time or scaling ranges. In order to analyze long-range dependent traffic with changing scaling exponents over time scales, we propose a multi-scale traffic model that incorporates the notion of a piecewise self-similar process, a process with spectral changes on its scaling behavior. We can obtain a performance curve smoothened over the range of queue length corresponding to time scales with different scaling exponents by adopting multiple self-similar processes piecewise into different spectra of time scale. The analytical method for the multiscale fractional Brownian motion is discussed as a model for this approach. A comparison of the analytical and simulation results, using traffic data obtained from backbone networks, shows that our model provides a good approximation for Gaussian traffic.

Two-dimensional phase unwrapping (PU) process usually causes a noise-induced distortion in the geographical information of a wrapped phase image obtained by, for example, interferometric synthetic aperture radar (InSAR). This paper presents a novel method to reduce the phase-unwrapping distortion by being based on two-dimensional fractional Brownian motion (fBm) theory. The method incorporates fractal geometry estimation with conventional global-transform PU. For the spatial-frequency spectrum of an observed phase image, we estimate the fractal dimension by assuming an almost constant dimension over the image. Then, according to the estimation, we compensate the distorted spectrum of the tentatively computed global PU result. We obtain a better topographical map as the inverse Fourier transform of the compensated spectrum. It is demonstrated that the proposed method increases the signal-to-noise ratio of PU results for simulated data with various noise levels. Evaluations on an actual InSAR phase image also show that the method significantly improves the quality of the conventional global-transform PU result, in particular in its fine structure.

This paper presents a new data hiding scheme under fractal image generation via Fourier filtering method for Computer Graphics (CG) applications. The data hiding operations are achieved in the frequency domain and a method similar to QAM used in digital communication is introduced for efficient embedding in order to explore both phase and amplitude components simultaneously. Consequently, this scheme enables us not only to generate a natural terrain surface without loss of fractalness analogous to the conventional scheme, but also to embed larger amounts of data into an image depending on the fractal dimension. This scheme ensures the correct decoding of the embedded data under lossy data compression such as JPEG by controlling the quantization exponent used in the embedding process.

This paper presents a new data hiding scheme via steganographic image transformation, which is different from conventional data hiding techniques. The transformation is achieved in the frequency domain and the concept of Fourier filtering method is used. An input image is transformed into a fractal image, which can be used in Computer Graphic (CG) applications. One of the main advantages of this scheme is the amount of data to be hidden (embedded) is equal to that of the host signal (generated fractal image) while it is in general limited in the conventional data hiding schemes. Also both the opened fractal image and the hidden original one can be properly used depending on the situation. Unauthorized users will not notice the "secret" original image behind the fractal image, but even if they know that there is a hidden image it will be difficult for them to estimate the original image from the transformed image. Only authorized users who know the proper keys can regenerate the original image. The proposed method is applicable not only as a security tool for multimedia contents on web pages but also as a steganographic secret communication method through fractal images.

We examine the effectiveness of shaping and policing mechanisms in reducing the inherent variability of fractal traffic, with the objective of increasing network operating points. Whether a shaper simply spaces a flow or allows small bursts according to a leaky bucket, we show using analytical arguments that, i) the Hurst parameter, which describes the asymptotic variability of the traffic, is unaffected; and ii) while the traffic can be made smoother over time scales smaller than one corresponding to the shapers buffer size, fluctuations over longer time scales cannot be appreciably altered. We further show that if shaping is used to reduce buffer size requirements at a network bottleneck, any savings here are offset by the increased buffer requirements at the shapers. Perhaps the most significant deficiency of shaping identified here is that it is necessary to model individual streams to a level of accuracy that is not feasible in practice. In contrast, statistical multiplexing can achieve reasonable network efficiencies by only requiring characterizations of aggregate traffic.