Title:

Methods for signal filtering and modelling and their parallel distributed computing implementation

In this thesis the problem of filtering and modelling onedimensional discrete signals and implementation of corresponding parallel distributed algorithms will be addressed. In Chapter 2, the research areas of parallel distributed computing environments, rankbased nonlinear filter and fractal functions are reviewed. In Chapter 3, an Interactive Parallel Distributed Computing Environment (IPDCE) is implemented based on Parallel Virtual Machine (PVM) and an interactive application development tool, the Tc1 language. The approach we use is to provide a Tc1 version interface for all procedures of the PVM interface library so that users can utilize any PVM procedure to do their parallel computing interactively. In Chapter 4, an interactive parallel stackfiltering system is implemented, based on the IPDCE. The user can play with this filtering system in both traditional command mode and modern Graphics User Interface (GUI) mode. In order to reduce the time required to compute a standard stack filter, a new minimum threshold decomposition scheme is introduced and other techniques such as minimizing the number of logical operations and utilizing the CPU bitfields parallel property are also suggested. In this filtering system the user can select sequential or parallel stackfiltering algorithms. The parallel distributed stackfiltering algorithm is implemented with equal task partitioning and PVM. Two numerical simulations show that the interactive parallel stackfiltering system is efficient for both the sequential and the parallel filtering algorithms. In Chapter 5, an extended Iterated Function System (IFS) interpolation method is introduced for modelling a given discrete signal. In order to get the solution of the inverse IFS problem in reasonable time, a suboptimal search algorithm, which estimates first the local selfaffine region and then the map parameters is suggested, and the neighbourhood information of a selfaffine region is used for enhancing the robustness of this suboptimal algorithm. The parallel distributed version of the inverse IFS algorithm is implemented with equal task partitioning and using a Remote Procedure Call application programming interface library. The numerical simulation results show that the IFS approach achieves a higher signal to noise ratio than does an existing approach based on autoregressive modelling for selfaffine and approximately selfaffine onedimensional signals and, when the number of computers is small, the speedup ratio is almost linear. In Chapter 6, inverse IFS interpolation is introduced to model selfaffine and approximately selfaffine onedimensional signals corrupted by Gaussian noise. Local crossvalidation is applied for compromising between the degree of smoothness and fidelity to the data. The parallel distributed version of the inverse algorithm is implemented in Parallel Virtual Machine (PVM) with static optimal task partitioning. A simple computing model is applied which partitions tasks based on only each computer's capability. Several numerical simulation results show that the new IFS inverse algorithm achieves a higher signal to noise ratio than does existing autoregressive modelling for noisy selfaffine or approximately selfaffine signals. There is little machine idle time relative to computing time in the optimal task partition mode. In Chapter 7, local IFS interpolation, which realises the IFS limit for selfaffine data, is applied to model non selfaffi.ne signals. It is difficult, however, to explore the whole parameter space to achieve globally optimal parameter estimation. A twostage search scheme is suggested to estimate the selfaffine region and the associated region parameters so that a suboptimal solution can be obtained in reasonable time. In the first stage, we calculate the selfaffine region under the condition that the associated region length is twice that of the selfaffine region. Then the second stage calculates the associated region for each selfaffine region using a full search space. In order to combat the performance degradation caused by the the difference of machines capabilities and unpredictable external loads, a dynamic loadbalance technique based on a data parallelism scheme is applied in the parallel distributed version of the inverse local IFS algorithm. Some numerical simulations show that our inverse local IFS algorithm works efficiently for several types of onedimensional signal, and the parallel version with dynamic load balance can automatically ensure that each machine is busy with computing and with low idle time.
