Medical Image Denoising Using Reinforced Gradient Minimization

Yıl 2023, , 163 - 176, 30.04.2023

Metin Ertas

https://doi.org/10.17482/uumfd.1139249

Öz

Medical images are naturally exposed to different types and levels of noise. The main purpose of algorithms used in the reconstruction of medical images is to use the most efficient method to remove this noise and to increase the resolution. With these techniques, the noise is intended to be removed using filters, regularizers, and noise removal operators. After the availability of compressed sensing in medical imaging, the total variation (TV) minimization, which transforms the image into a sparser form, reduces the image noise and preserves small details and edges. In this study, a local gradient operator TD has been redesigned as a stronger noise remover by increasing the level of the neighborhood used in partial gradient directions. The proposed reinforced gradient minimization's ability to reduce noise under various levels of Gaussian, Poisson, and Gauss+Poisson noise was compared to that of the traditional TV technique. The results were compared using peak signal-to-noise-ratio (PSNR), structure similarity (SSIM), contrast-to-noise-ratio (CNR) metrics, and visual analysis. It was shown that the proposed reinforced gradient minimization method has better noise removal potential than that of the TV algorithm.

Anahtar Kelimeler

total variation, image denoising, Gaussian, Poisson, reinforced gradient minimization

GÜÇLENDİRİLMİŞ GRADYAN MİNİMİZASYONU KULLANARAK MEDİKAL GÖRÜNTÜLERDE GÜRÜLTÜ ARINDIRMA

Öz

Medikal görüntüler doğası gereği farklı gürültü tipleri ve seviyelerine maruz kalmaktadır. Medikal görüntülerin oluşturulmasında kullanılan rekonstrüksiyon algoritmalarının temel amacı, oluşan bu gürültünün giderilmesi ve çözünürlüğün arttırılması için en verimli yöntemlerin kullanılmasıdır. Bu yöntemler kullanılırken filtreleme, düzenleyiciler ve gürültü giderici operatörler kullanıp gürültünün arındırılması amaçlanmaktadır. Sıkıştırılmış algılamanın medikal görüntülemede aktif olarak kullanılmaya başlanmasından sonra, görüntüyü daha seyrek forma dönüştüren toplam değişinti (TD) en küçüklemesi ile görüntü üzerindeki gürültü azaltılarak ufak detayların ve kenarların daha net biçimde korunması sağlanmıştır. Lokal bir gradyan operatörü olan toplam değişinti algoritması bu çalışmada kısmi gradyan yönlerinde kullanılan komşuluk seviyesi arttırılarak daha güçlü bir gürültü giderici olarak yeniden tasarlanmıştır. Çalışma kapsamında, tasarlanan bu yeni güçlendirilmiş gradyan minimizasyonunun medikal görüntülerde mevcut farklı Gauss, Poisson ve Gauss+Poisson gürültü seviyeleri üzerinde gürültü arındırma başarısı klasik TD ile karşılaştırılmıştır. Sonuçlar pik sinyal-gürültü oranı, yapısal benzerlik ve kontrast-gürültü oranı metrikleri ve görsel analiz kullanılarak karşılaştırılmış ve önerilen yeni güçlendirilmiş gradyan minimizasyonu yönteminin mevcut klasik TD algoritmasından daha iyi gürültü arındırma potansiyeline sahip olduğu gösterilmiştir.

Anahtar Kelimeler

toplam değişinti, gürültü arındırma, Gauss, Poisson, güçlendirilmiş gradyan minimizasyonu

Kaynakça

• 1. Boyd S, Parikh N, Chu E, Peleato B, Eckstein J., (2011) “Distributed optimization and statistical learning via the alternating direction method of multipliers” vol. 3. https://doi.org/10.1561/2200000016.
• 2. Candes E.J., Wakin M.B., andBoyd S.P., (2008) “Enhancing sparsity by reweighted l1 minimization,” J. Fourier Anal. Appl., vol. 14, pp. 877–905. https://doi.org/10.1007/s00041- 008-9045-x
• 3. Chen Z, Jin X, Li L, Wang G. A, (2013) “limited-angle CT reconstruction method based on anisotropic TV minimization.” Phys Med Biol; 58:2119. https://doi.org/10.1088/0031- 9155/58/7/2119
• 4. Cheng Z., Chen Y., Wang L., Lin F., Wang H. and Chen Y., (2018), "Four-Directional Total Variation Denoising Using Fast Fourier Transform and ADMM," IEEE 3rd International Conference on Image, Vision and Computing (ICIVC), pp. 379-383, doi: 10.1109/ICIVC.2018.8492869
• 5. Gilboa G., Sochen N., Zeevi Y.Y., (2006) “Variational denoising of partly textured images by spatially varying constraints”, IEEE Trans. on Image Processing, vol. 15, no. 8, pp. 2281-2289. doi: 10.1109/TIP.2006.875247.
• 6. Guo Y., Zeng L., Wang C. , Zhang L., (2017), “Image reconstruction model for the exterior problem of computed tomography based on weighted directional total variation”, Applied Mathematical Modelling, 52 (358: 377), https://doi.org/10.1016/j.apm.2017.07.057.
• 7. Huang Y, Taubmann O, Huang X, Haase V, Lauritsch G, Maier, (2016) “A new weighted anisotropic total variation algorithm for limited angle tomography.” , Proc of Int Symp Biomed Imaging 2016; 585–8. https://doi.org/10.1109/ISBI.2016.7493336.
• 8. Huang Y, Taubmann O, Huang X, Haase V, Lauritsch G, Maier, (2018), “A. Scale-space anisotropic total variation for limited angle tomography. IEEE Trans Radiat Plasma Med Sci; 2:307–14. https://doi.org/10.1109/TRPMS.2018.2824400.
• 9. Joshi, S. H., Marquina, A., Osher, S. J., Dinov, I., Van Horn, J. D., & Toga, A. W. (2009). “MRI Resolution Enhancement Using Total Variation Regularization”. Proceedings. IEEE International Symposium on Biomedical Imaging, 2009, 161–164. https://doi.org/10.1109/ISBI.2009.5193008
• 10. Liao F., Coatrieux J. L., Wu J., and Shu H., (2015),‘‘A new fast algorithm for constrained four-directional total variation image denoising problem,’’ Math. Problems Eng., vol. 2015, pp. 1–11, https://doi.org/10.1155/2015/815132
• 11. Miao C and Yu H. (2015), “A General-Thresholding Solution for lp(0<p<1) Regularized CT Reconstruction.” IEEE Trans Image Process; 24:5455–68. https://doi.org/10.1109/TIP.2015.2468175.
• 12. Motwani, M.C., Gadiya, M.C., Motwani, R.C. and Harris, F.C., (2004), “Survey of image denoising techniques.” In Proceedings of GSPX (Vol. 27, pp. 27-30).
• 13. Pang Z.F., Zhou Y.M., Wu T., Li D.J., (2019), “Image denoising via a new anisotropic total-variation-based model”, Signal Processing: Image Communication, 74, (140-152), https://doi.org/10.1016/j.image.2019.02.003.
• 14. Qu Z., Zhao X., Pan J. and Chen P., (2019), “Sparse-view CT reconstruction based on gradient directional total variation”, Meas. Sci. Technol., 30, 055404, https://doi.org/10.1088/1361-6501/ab09c6 .
• 15. Rudin L., Osher S., Fatemi E., (1992), “Nonlinear total variation based noise removal algorithms”, Physica D 60 (1–4) 259–268. https://doi.org/10.1016/0167-2789(92)90242-F
• 16. Sakurai M., Kiriyama S., Goto T., and Hirano S., (2011)‘‘Fast algorithm for totalvariationmminimization,’’ in Proc. 18th IEEE Int. Conf. Image Process., pp. 1461–1464, doi:m10.1109/ICIP.2011.6115718.
• 17. Sidky E Y, Kao C-M and Pan X (2006) “Accurate image reconstruction from few-viewsmand limited-angle data in divergent-beam CT” J. X-Ray Sci. Technol. 14 119–39
• 18. Sidky EY, Pan X. (2008), “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization.” Phys Med Biol;53:4777. https://doi.org/10.1088/0031-9155/53/17/021.
• 19. Sidky E.Y., Reiser I., Nishikawa R.M., Pan X., Chartrand R., Kopans D.B., (2008), “Practical iterative image reconstruction in digital breast tomosynthesis by non-convex TpV optimization.” Med Imaging 2008 Phys Med Imaging; 6913:691328. https://doi.org/10.1117/12.772796.
• 20. Wang, Z., Simoncelli, E.P., Bovik, A.C., (2003), “Multiscale structural similarity for image quality assessment”, The Thrity-Seventh Asilo-mar Conference on Signals, Systems Computers, 2003, pp. 1398–1402 Vol.2. doi: 10.1109/ACSSC.2003.1292216.
• 21. Wang T., Nakamoto K., Zhang H. and Liu H., (2017), "Reweighted Anisotropic Total Variation Minimization for Limited-Angle CT Reconstruction," in IEEE Transactions on Nuclear Science, vol. 64, no. 10, pp. 2742-2760, doi: 10.1109/TNS.2017.2750199.
• 22. Wu L., Chen Y., Jin J., Du H., and Qiu B., (2017),‘‘Four-directional fractional order total variation regularization for image denoising,’’ J. Electron Imag., 26 (5, doi: 10.1117/1.JEI.26.5.053003.
• 23. Yan K., Wang X., Lu L., and Summers R.M., (2018) “DeepLesion: automated mining of large-scale lesion annotations and universal lesion detection with deep learning.” J Med Imaging, 5(3):036501. doi: 10.1117/1.JMI.5.3.036501.
• 24. Zhang Z., Chen B., Xia D., Sidky E.M. and Pan X., (2021), “Directional-TV algorithm for image reconstruction from limited-angular-range data”, Medical Image Analysis, 70,102030, https://doi.org/10.1016/j.media.2021.102030
• 25. Zheng J., Fessler J.A., Chan H-P. (2016); “Digital breast tomosynthesis reconstruction using spatially weighted non-convex regularization.” Med Imaging 2016 Phys Med Imaging;9783:978369. https://doi.org/10.1117/12.2216414.