An Analysis of Oscillator-Based Computations for Image Processing

Although there has been a vast amount of research into improving CMOS technology and computer architecture to make more powerful and efficient systems, the trends of decreasing sizes and energy and increasing power and speed are plateauing. Major roadblocks hindering the progression of Boolean logic based computing are transistor size, heat dissipation, clock speed, and computation power. This has inspired investigation into new methods for performing, complex operations not based on logic gates, or non-Boolean computations. One such method is coupled oscillator arrays. Instead of a logic gates to compute complex functions, the intrinsic physical properties of the oscillators can be used for computation making them more efficient for non-Boolean computations. This thesis will explore the use of coupled oscillator arrays to perform convolution, a primitive operation that plays a central role in many signal and image processing algorithms. Real-world circuit model parameters will be discussed and their impact on the circuit will be analyzed. In addition, this thesis will show the use of oscillators in Degree of Match (template matching), discrete cosine transform, discrete Fourier transform, Gabor filtering, and image compression. The effects of the model parameters on the will be examined on these implementations

Synchronization Analysis of Winner-Take-All Neuronal Networks

With the physical limitations of current CMOS technology, it becomes necessary to design and develop new methods to perform simple and complex computations. Nature is efficient, so many in the scientific community attempt to mimic it when optimizing or creating new systems and devices. The human brain is looked to as an efficient computing device, inspiring strong interest in developing powerful computer systems that resemble its architecture and behavior such as neural networks. There is much research focusing on both circuit designs that behave like neurons and arrangement of these electromechanical neurons to compute complex operations. It has been shown previously that the synchronization characteristics of neural oscillators can be used not only for primitive computation functions such as convolution but for complex non-Boolean computations. With strong interest in the research community to develop biologically representative neural networks, this dissertation analyzes and simulates biologically plausible networks, the four-dimensional Hodgkin-Huxley and the simpler two-dimensional Fitzhugh-Nagumo neural models, fashioned in winner-take-all neuronal networks. The synchronization behavior of these neurons coupled together is studied in detail. Different neural network topologies are considered including lateral inhibition and inhibition via a global interneuron. Then, this dissertation analyzes the winner-take-all behaviors, in terms of both firing rates and phases, of neuronal networks with different topologies. A technique based on phase response curve is suggested for the analysis of synchronization phase characteristics of winner-take-all networks. Simulations are performed to validate the analytical results. This study promotes the understanding of winner-take-all operations in biological neuronal networks and provides a fundamental basis for applications of winner-take-all networks in modern computing systems

Computing With Hybrid Material Oscillators

The evolution of computers is driven by advances not only in computer science, but also in materials science. As the post-CMOS era approaches, research is increasingly focusing on flexible and unconventional computing systems, including the study of systems that incorporate new computational paradigms into the materials, enabling the computer and the material to be the same entity. In this dissertation, we design a coupled oscillator system based on a new hybrid material that can autonomously transduce chemical, mechanical, and electrical energy. Each material unit in this system integrates a self-oscillating gel, which undergoes the Belousov-Zhabotinsky (BZ) reaction, with an overlaying piezoelectric (PZ) cantilever. The chemo-mechanical oscillations of the BZ gels deflect the piezoelectric layer, which consequently generates a voltage across the material. When these BZ-PZ units are connected in series by electrical wires, the oscillations of these coupled units become synchronized across the network, with the mode of synchronization depending on the polarity of the piezoelectric. Taking advantage of this synchronization behavior, we demonstrate that the network of coupled BZ-PZ oscillators can perform specific computational tasks such as pattern matching in a self-organized manner, without external electrical power sources. The results of the computational modeling show that the convergence time for stable synchronization gives a distance measure between the “stored” and “input” patterns, which are encoded by the connection and phases of BZ-PZ oscillators. In addition, we demonstrate two methods to enrich the information representation in our system. One is to employ multiple BZ-PZ oscillator networks in parallel and to process information encoded in different channels. The other is to introduce capacitors into a BZ-PZ network that modify the dynamical behavior of the systems and increase the information storage. We analyze and simulate the proposed coupled oscillator systems by using linear stability analysis and phase models and explore their potential computational capabilities. Through these studies, we establish experimentally realizable design rules for creating “materials that compute”