Image Reconstruction by the Method of Reverse Projection Using Wavelet Filtering of Projection Data in X-ray Computed Tomography
DOI:
https://doi.org/10.14529/cmse240201Keywords:
X-ray computed tomography, projection data, waveletsAbstract
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.References
Luitt R.M. Reconstruction algorithms using integral transformations. TIIER. 1983. Vol. 71, no. 3. P. 125–148.
Louis A.K., Netterer F. Mathematical problems of reconstructive computational tomography. TIIER. 1983. Vol. 71, no. 3. P. 111–125.
Barrett J.E., Keant N. Artifacts in CT: Recognition and Avoidance. Radio Graphics. 2004. Vol. 24. P. 1679–1691. DOI: 10.1148/rg.246045065.
Arsenin V.Ya., Kriksin Yu.A., Timonov A.A. Method of local regularization of linear operator equations of the first kind and its applications. Computational mathematics and mathematical physics. 1988. Vol. 28, no. 6, P. 793–808.
Pikalov V.V., Nepomnyashchy A.V. Iterative algorithm with wavelet filtering in a two-dimensional tomography problem. Computational methods and programming. 2003. Vol. 4, no. 1. P. 244–253.
Voskoboynikov Yu.E., Kolker A.B. Combined algorithms for filtering noisy signals and images. Autometry. 2002. No. 4. P. 51–60.
Voskoboinikov Yu.E., Bronnikov A.V. Adaptive image filtering algorithm and image conversion to vector format. Autometry. 1990. No. 1. P. 124–132.
Voskoboynikov Yu.E., Belyavtsev V.G. Image filtering algorithms with aperture size adaptation. Autometry. 1998. No. 3. P. 81–89.
Simonov E.N. Physics of image visualization in X-ray computed tomography. Chelyabinsk: SUSU Publishing House, 2014. 479 p.
Laskov V.V., Simonov E.N. Methods of image filtering in X-ray computed tomography. Bulletin of the South Ural State University. Computer Technologies, Control, Radio Electronics. 2014. Vol. 14, no. 3. P. 29–33.
Laskov V.V., Simonov E.N. Reduction of ring artifacts in computer tomography. Biomedical Engineering. 2016. Vol. 49, no. 5. P. 274–277. DOI: 10.1007/s10527-016-9547-9.
Bessonov V.B., Klonov V.V., Larionov I.A., Staroverov N.E. Development of a method for correcting metal artifacts in tomographic studies. Physical fundamentals of instrumentation. 2020. Vol. 9, no. 4(38). P. 54–59. DOI: 10.25210/jfop-2004-054059.
Bessonov V.B., Potrakhov N.N., Obodovsky A.V. X-ray tomography. Photonics. 2019. No. 7. P. 688–693. DOI: 10.22184/1992-7296.FRos.2019.13.7.688.692.
Klonov V.V., Larionov I.A., Bessonov V.B., Baksheev I.K. Development of x-ray dose sensor. AIP Conference Proceedings. 2021. Vol. 2356, no. 1. P. 020013. DOI: 10.1063/5.0053146.
Staroverov N.E., Gryaznov A.Y., Bessonov V.B. Research of the possibility of using neural networks to identify areas of interest in tomographic data. AIP Conference Proceedings. 2020. Vol. 2250, no. 1. P. 020027. DOI: 10.1063/5.0013424.
Obodovskiy A.V., Bessonov V.B., Larionov I.A. Features of the practical application of microfocus x-ray tomograph in biomedical engineering. AIP Conference Proceedings. 2019. Vol. 2140, no. 1. P. 020049. DOI: 10.1063/1.5121974.
Daubechies I. The wavelet transform, time-frequency localization and signal analyses. IEEE Trans. Inform. Theory. 1990. Vol. 36, no. 36. P. 961–1005. DOI: 10.1109/18.57199.
Donoho D. Nonlinear solution of linear inverse problems by wavelet-vaguelette decompositions. Journal of Applied and Computational Harmonic Analysis. 1995. Vol. 2, no. 2. P. 101–126. DOI: 10.1006/acha.1995.1008.
Birge L., Massart P. From model selection to adaptive estimation. Festschrift for Lucien Le Cam / eds. by D. Pollard, E. Torgersen, G.L. Yang. Springer, 1997. Р. 55–88. DOI: 10.1007/978-1-4612-1880-7_4.
Chang S., Yu B., Vetterli M. Spatially adaptive wavelet thresholding with context modeling for image denoising. IEEE Transactions on Image Processing. 2000. Vol. 9, no. 9. Р. 1522–1531. DOI: 10.1109/83.862630.
Simonov E.N. Certificate of state registration of software No. 2011612631 “Tomographic Image Reconstructor” issued on 31.04.2011.
Shi H., Luo S., Yang Z.,Wu G. A Novel Iterative CT Reconstruction Approach Based on FBP Algorithm. PLOS One. 2015. Vol. 10, no. 9. P. e0138498. DOI: 10.1371/journal.pone.0138498.
