Image reconstruction by the method of reverse projection using wavelet filtering of projection data in x-ray computed tomography

The article presents a method for reducing the error of image reconstruction for X-ray computer tomography by using wavelet filtering of noisy projection data. The wavelet transformation and the wavelet filtering of one-dimensional signals based on it makes it possible to determine a specific place of correspondence between the frequency and time (in this case, the spatial coordinate of the detectors) region. This makes it possible to uniquely determine the transition from the frequency domain to the spatial domain and vice versa. To filter the projection data, the wavelet transform is used, which makes it possible, through coefficients defining scaling functions and wavelet functions, to determine in the frequency and spatial domain the place of noise in a noisy signal and to isolate a non-noisy signal by assigning filtering thresholds to the above coefficients. To enhance the filtering properties of the wavelet transform, it is proposed to divide the projection data into intervals, for each of which its coefficients are determined. Wavelet filtering is carried out using Daubeshi wavelets. The research results were confirmed by mathematical modeling of noisy projection data, their wavelet filtering and reconstruction of the test tomographic image based on them. The mathematical model of the test object of the study and the software reconstructor of the tomographic image developed by the authors made it possible to simulate direct (obtaining projection data on the test object), reverse (obtaining a test tomographic image from the projection data of the object) tomography tasks and to carry out a comparative analysis of the quality of image reconstruction with “ideal” and noisy projection data.