Image Filtering And Detection Based On Fractional Lower Order Statistics

Fractional lower order moment (FLOM) which also is called as fractional lower order statistics (FLOS) is one forceful tool of non-Gaussian signal analysis and processing. Using the research method based on FLOS for image project has important actual significance. The dissertation sets forth the theory ofαstable distribution corresponding to the theory of FLOS firstly and then introduces various algorithms based on the theory of FLOS. On the basis of these algorithms, that FLOS is used for image processing is studied. Main research work of this dissertation includes followings:(1) The dissertation uses FLOS theory and applies effective methods of negative order moment and logarithmic order moment to estimate the parameterαandγof the two-dimensional (2-D) wavelet coefficients of supersonic medicine image. The experimental data indicates that these two methods can effectively estimate the parameterαandγof the 2-D wavelet coefficients which satisfy the symmetricalαstable (SαS) distribution. It shows that in actual image processing, we must consider the non-Gaussian characteristics of signal to avoid the performance degeneration of using the conventional signal processing method and it is benefit for the following processing for images. For example, it builds up foundation for mixing Bayesian estimation and wavelet threshold to eliminate noise.(2) Based on work (1) and the wavelet threshold value method brought forward by many scholars, FLOS theory, signal detection and parameter estimation theory are combined to introduce the mixed method of Bayesian estimation and wavelet threshold to eliminate noise for supersonic medicine image based onαstable distribution, that is, using Bayesian estimation to well extract the low frequency wavelet coefficients of the image, and using wavelet soft threshold processing for the high frequency coefficients, then restoring the signal by the inverse wavelet transform. Comparing with the former method, we can obtain the significant conclusion. The experimental data indicates that this method is superior to that only the wavelet threshold value method is used, which enormously enhances SNR and has the better filter effect. (3) On the foundation of the simplest classical method—the least mean square (LMS) algorithm, this dissertation brings forward the different effective methods that we can obtain based on FLOS by changing the algorithm parameter—the optimal toughness mixed p-norm filtering algorithm to filter the additive noise which satisfies theαstable distribution in images. Then it carries on comparison and analysis to obtain the significant conclusion. The theoretical analysis and the computer simulation result indicate that this method has good toughness and moreover some effective classical algorithms can be obtained after setting the algorithm parameter.(4) On the foundation of Gaussian distribution, this dissertation combines FLOS and mathematics morphology, takes the supersonic medicine image as the example, uses Gaussian distribution method and theαstable distribution method respectively to carry on the threshold detection, then plots the granularity distribution function of the horizontal direction and that of the vertical direction respectively, and extracts correlation coefficients of two directions. Then the dissertation shows superiority of threshold detection based on FLOS.In a word, the method based on FLOS has better toughness and more significance than the method based on Gaussian ditribution.The method based on Gaussian ditribution is one special mode of the method based on FLOS. The method based on FLOS will indicate its superiority in image processing.