There exist some variations of the particle swarm optimization -simulated annealing optimization technique (PSOSA) hybrid algorithm for solving the PID control design problem, however most of these algorithms use the simulated annealing as a tool to escape local minimums that the PSO algorithm may get trapped in and also these algorithms initialize the particles within the solution space randomly. In this paper, the effects of initializing the particles strategically within the solution space along with the application of the SA algorithm to the hybrid algorithm at each iteration are explored. To test the effectiveness of the proposed modifications the algorithms are compared on common benchmark functions before the modified hybrid algorithm (MPSOSA) is used to design a PID controller for the inverted Pendulum problem.

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Complex signals such as images, audio and video recordings can be represented by a large over-complete dictionary without significant compromise on the representation quality. An over-complete dictionary has many more columns than the number of rows. Large over-complete dictionaries can produce sparse representation vectors and provide significant improvements in the reconstructed signal quality because it contains many patterns to select from. The use of the over-complete dictionaries and sparse coding has been successfully applied in compression, de-noising, and pattern recognition applications within the last few decades. An example of an over-complete dictionary that has seen a great deal of success in image processing applications is the Discrete Cosine Transform (DCT) dictionary. However, we propose a novel non-linear overcomplete dictionary that improves the quality of the signal representation while reducing the number of non-zero elements to represent the signal. The proposed non-linear dictionary has demonstrated through experimental results to be superior to the DCT dictionary by achieving higher signal to noise ratio (SNR) in the reconstructed images.

There has been a growing interest in the different types of dictionaries that can be used in image processing applications. We propose a hybrid dictionary composed of transform based atoms and additional nonlinear atoms generated using the polynomial, rectangular and exponential functions. The additional nonlinear atoms improve signal reconstruction quality for both transient and smooth signals. To further improve signal reconstruction quality, we optimize the hybrid dictionary using training samples from the signal. We also propose a signal coding algorithm that generates additional atoms by performing a circular shift on the provided dictionary prior to coding the signal. We have evaluated the proposed methods against existing predefined dictionaries by visually examining the reconstructed images as well as evaluating the peak signal to noise ratio of the reconstructed signal. All methods proposed in this thesis improved signal reconstruction quality however; we require an in-depth cost analysis study to evaluate its limitations.

There has been a growing interest in the different types of dictionaries that can be used in image processing applications. We propose a hybrid dictionary composed of transform based atoms and additional nonlinear atoms generated using the polynomial, rectangular and exponential functions. The additional nonlinear atoms improve signal reconstruction quality for both transient and smooth signals. To further improve signal reconstruction quality, we optimize the hybrid dictionary using training samples from the signal. We also propose a signal coding algorithm that generates additional atoms by performing a circular shift on the provided dictionary prior to coding the signal. We have evaluated the proposed methods against existing predefined dictionaries by visually examining the reconstructed images as well as evaluating the peak signal to noise ratio of the reconstructed signal. All methods proposed in this thesis improved signal reconstruction quality however; we require an in-depth cost analysis study to evaluate its limitations.