Volterra-type nonlinear filtering for medical imaging enhancements using principal dynamic modes

The objective of this dissertation is to develop a tool for the investigation of nonlinear imaging system. Volterra-type filtering for the enhancement of medical images obtained via a novel transmission-mode ultrasonic system was explored and its efficacy was verified by feasibility studies. The images obtained from the High-resolution Ultrasonic Transmission Tomography (HUTT) system were compared with optical and MR images of the same phantoms. The efficacy of the Volterra filtering approach was examined in the projection profile (sinogram) domain (1-D) and in the image domain (2-D).; The use of Volterra-type filtering was investigated in the image domain by estimating up to the 3rd-order Volterra kernels and the validity and efficacy of this technique were demonstrated with phantom data from the HUTT system. An important advantage of this technique over other conventional methods is that it avoids inversion of the image degradation process.; For the 2-D implementation of Volterra filtering, we have designed 2-D discrete Hermite basis functions, which are based on models of receptive fields profiles of the human visual system. Using these basis functions the efficiency of the estimation of the Volterra filters increases significantly.; The concept of Principal Dynamic Modes (PDMs) made it possible to explore the higher order nonlinear dynamics of system that compact the representation of high-order kernels. The PDMs constitute the optimum filter bank for a specific system in terms of Normalized Mean Square Error (NMSE) rate of decrease and were shown to yield good results when applied to HUTT images of various phantoms and real tissue in mapping onto other modality images (optical and MR) for the improvement of image quality.