Infinitely Divisible Cascades to Model the Statistics of Natural Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Workload dynamics on clusters and grids
The Journal of Supercomputing
Multifractal random walks as fractional Wiener integrals
IEEE Transactions on Information Theory
Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes
Journal of Mathematical Imaging and Vision
| Hi-index | 754.90 |
Multiplicative processes, multifractals, and more recently also infinitely divisible cascades have seen increased popularity in a host of applications requiring versatile multiscale models, ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. The methodologies prevalent as of today rely to a large extent on iterative schemes used to produce infinite detail and repetitive structure across scales. While appealing, due to their simplicity, these constructions have limited applicability as they lead by default to power-law progression of moments through scales, to nonstationary increments and often to inherent log-periodic scaling which favors an exponential set of scales. This paper studies and develops a wide class of infinitely divisible cascades (IDC), thereby establishing the first reported cases of controllable scaling of moments in non-power-law form. Embedded in the framework of IDC, these processes exhibit stationary increments and scaling over a continuous range of scales. Criteria for convergence, further statistical properties, as well as MATLAB routines are provided.