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Self-similar random fields are of interest in various areas of image processing since they fit certain types of natural pat- terns and textures. Current treatments of self-similarity in continuous two-dimensional (2-D) space use a definition that is a direct extension of the one-dimensional definition, which requires invariance of the statistics of a random process to time scaling. Current discrete-space 2-D approaches do not consider scaling, but, instead, are based on ad hoc formulations, such as digitizing continuous random fields. In this paper, we show that the current statistical self-similarity definition in continuous space is restrictive and provide an alternative, more general definition. We also provide a formalism for discrete-space statistical self-similarity that relies on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields and texture images. [ABSTRACT FROM AUTHOR]

This paper proposes a simulation model based on the fact that 1/ f processes belong to the class of statistically self-similar random processes. Unlike most of the earlier modeling approaches, which were confined to the spectral domain, the model generates 1/ f noise in the time domain with a simple white noise input and is parameterized by a quantity whose value can be adjusted to reflect the desired slope of the 1/ f spectrum. To verify the fit between the model and actual 1/f noise measurements, experiments were conducted with a p-i-n photodiode at various bias conditions and sampling frequencies. [ABSTRACT FROM AUTHOR]

Wide-sense statistical self-similarity in continuous-time random processes is defined through invariance of its first-order and second-order statistics to scaling in time. Since scaling has an unambiguous definition in continuous-time but not in discrete-time, researchers have provided various definitions of discrete-time self-similarity without reference to scaling. This paper proposes a discrete-time continuous-dilation scaling operator and develops a framework based on it for formulating statistical self-similarity from first principles in a manner analogous to the continuous-time development. Relationship between the resulting model and fractional order transfer function systems is presented. The potential for using this model in applications involving long-range dependent phenomena is explored. [ABSTRACT FROM AUTHOR]

Focuses on a study which investigated the application of discrete-time statistically self-similar systems to modeling variable-bit rate (VBR) video traces. Characteristics of VBR video traffic; Discrete-time self-similarity; Stable distributions.

Deals with a study which developed a bandlimited orthonormal wavelet for applications requiring a matched filter approach. Analysis of the orthonormal multiresolution analysis (MRA); Discussion on signal detection; Properties of a wavelet in an orthonormal MRA.

Deals with approximation and interpolation sampling systems. Interpolation and approximation sampling systems matched to the input process; Explanation on the perfect reconstruction circular convolution framework; Conclusion.