| The goal of this thesis is to examine various applications and forms of nonlinear filter banks for image processing. Depending on the application needs, this thesis examines the utility of nonlinear filter banks. In doing so, we attempt to provide alternatives to the conventional linear filter bank by improving computational complexity, objective and/or subjective image quality, and storage requirements.; The ability to perform nonlinear operations is once again a nontrivial problem. Within the area of compression, compaction of the image is critical to perform significant processing operations. We have addressed the issues of compaction, maximal decimation and perfect reconstruction in the nonlinear context. Through this investigation, we have determined areas where nonlinear filter banks offer benefits to image processing. In the area of compression, this thesis will introduce two nonlinear filter banks. The first is a finite field filter bank which, through nonlinear operations, constrains the dynamic range of the subband outputs. The intent of this filter bank is to reduce both the computational complexity and the first order entropy. Second, we developed a nonlinear nonuniform filter bank. This filter bank is intended to improve both objective and subjective quality in the presence of quantization.; Finally, we have merged the ideas of the rectangular nonlinear filter banks and the finite field filter banks to develop a new binary directional filter bank. This filter bank is a maximally decimated, perfectly reconstructing and field-order limited system that decomposes an image into its directional features. Finally, we have applied this filter bank to areas of object recognition and image enhancement. We show that such filter banks can provide a useful representation for character and target recognition. In addition we show that the analysis-synthesis properties of the system can be used to enhance the quality of binary characters. |
