Application of wavelet analysis for processing tomograms of narrow cracks

Abstract

Abstract The previously proposed method of increasing the visibility of cracks on tomograms obtained from X-ray sensing of sections of metal elements of building structures has been developed. A multiscale decomposition of tomogram lines is performed using the Haar wavelet basis. The detailed decomposition coefficients corresponding to the level of the assumed crack width are multiplied by a constant, the value of which is determined based on the noise level and the difference between the amplitude of the crack image and the surrounding background. In contrast to the previous work, where these parameters were assumed to be set, here we suggest the methods for its evaluating from the measurements. In particular, a simple formula is obtained that relates the variance of uncorrelated noise in the projection data to that of noise in the tomogram. The method is implemented as a computational algorithm based on which a computer program is developed. Numerical modeling was performed. The errors of the first and second kind were used toevaluate the effectiveness of the method determining whether a pixel belongs to a crack image. Binary classification was used for their calculation. Dependences of errors on the number of projections and the noise level on them were obtained. The results of the simulations showed that the use of the proposed method can reduce errors by 1.7-2.5 times.