Data fusion techniques are beginning to attract considerable attention. In the NDE context, such techniques can be used to combine information from two or more NDE test methods to improve the probability of detection and enhance characterization results. An example of such an application involves the fusion of eddy current and ultrasonic NDE data. The eddy current phenomena relies on the diffusion process to propagate energy. Ultrasonic phenomena, in contrast, rely on wave propagation. The manner in which the energy interacts with the material under test is fundamentally different. It can therefore be argued that each test method provides a different perspective and consequently approaches that allow data from the two test methodologies to be fused have the potential for offering an improved understanding of the condition of the material;This dissertation presents an incremental step towards the development of a very novel phenomenological approach to data fusion. The method involves mapping of the wave field to a diffusion field using Q-transforms. The transformed and diffusion fields are then combined to synthesize the fused image. A systematic study of the issues involved in fusion and the registration of the data was conducted. The study was accomplished by developing and using a two-dimensional analytical model that includes both the diffusion and wave propagation contributions. The ultrasonic tests were simulated using an existing finite element model. The dissertation presents results obtained by transforming the ultrasonic data into the diffusion domain. The effect of Q-transform properties, especially its time shift property, on data registration is analyzed. A modified version of the Q-transform is also presented to overcome the problems associated with large differences in the values of the underlying partial differential equation coefficients. Theoretical results obtained using the approach together with a discussion on additional work that needs to be undertaken are presented.