| In numerous fields, from defense and security to medicine to robotics, success in signal processing applications is typically achieved through the use of tools originally designed to operate on multi-bit gray-level data. Standard representations of this input data, such as those achieved by the common Fourier, Wavelet, and cosine transforms, are primarily restricted to gray-level values, and are unable to properly function on binary data. Therefore, a need exists for similar representation schemes applicable to the binary domain, as such a formulation would provide the opportunity for enhancements in the current procedures for processing these signal types. In this thesis, logical transforms are explored and their ability to create useful representations of the binary input data is demonstrated to be analogous with the gray-level forms. Through the introduction of new transforms, representations, and non-linear algorithms as well as the application of these developments to binary signals, it is shown that the logical transforms and methodologies employed in this work outperform classic binary techniques for several major areas of digital signal processing (filtering, edge detection, and interpolation), as indicated by both a minimization in algorithm complexity and increased functional accuracy. Further extensions to this model are included, allowing the binary processes presented to operate on gray-level input data as well, showing broad versatility over the traditional methods. |
