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Abstract
This thesis addresses the current, largely unsatisfied, practical demand for efficient, realizable, minimal distortion storage methods for large volumes of digital imagery data. It employs and extends the standard linear predictive coding (LPC) methodology from 1-D to 2-D to encompass digital imagery data both analytically and experimentally. When appropriately employed, these predictive techniques demonstrate that significant savings in digital imagery storage resources are achievable with minimal attendant loss of fidelity. Specifically, the 2-D coding techniques realized herein are suitable for real-time applications with performance comparable to that realized in 1-D applications using the Minimum Mean Square Error (MMSE) fidelity criterion.
Several heretofore uncombined and novel approaches to the imagery compression problem are utilized including 2-D lattice finite impulse response (FIR) and infinite impulse response (IIR) filtering, reflection calculation using a modified Burg harmonic-mean method, adaptive Max quantization, and entropy coding. The system is completely simulated in software and designed with the strict constraints of realizability and real-time operation. In addition, numerical results are obtained for various size filters and types of input data. Image enhancement techniques are employed to remove image distortions by the compression process.
Results obtained indicate that 2-D reflection coefficients are a good means of characterizing imagery, and a new in-place parallel processing algorithm is derived and implemented for performing the required real-time 2-D FIR and IIR filtering computations. An 80-90 percent reduction in digital data storage is realized when using at least a 4-stage 2-D LPC filter. This compares favorably with existing transform-based techniques and requires significantly fewer computations. Finally, these 2-D LPC techniques are extended to additional dimensions and shown suitable for solution of the general multivariate modeling problem.
