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Difüz Optik Tomografi’de Modellenmiş Meme Tümörü Benzeri Dokuların Teşhisi için Simülasyon Deneyleriyle Geri Çatım Algoritmalarının Uygulanması

Yıl 2021, Cilt: 9 Sayı: 6 - ICAIAME 2021, 167 - 176, 31.12.2021

Gençay Sevim Yiğit Ali Üncü Murat Canpolat

https://doi.org/10.29130/dubited.1016284

Öz

Difüz Optik Tomografide (DOT), yüksek kaliteli görüntüler elde etmek için veri işleme ve geri çatım aşamaları çok önemlidir. Bu nedenle, sistem için uygun algoritmaların belirlenmesi kritik bir seçimdir. Bu çalışma, DOT görüntüleme için uygun bir geri çatım algoritmasını belirlemeyi amaçlamaktadır. DOT sistemlerinde kullanılan birçok geri çatım algoritması vardır. Bazı algoritmalar belirli özel durumları çözmek için geliştirilmiştir ve bazılarının da hala iyileştirilmesi gerekmektedir. Bu çalışmada, geri çatım işlemi için üç algoritma kullanılmıştır; Tekil Değer Ayrışımı (SVD), Bi-Konjuge Gradyan (Bi-CG) ve Transpozesiz Yarı Minimal Rezidüel (TFQMR). Algoritmaların test edilmesinde simülasyon deneylerinin verileri kullanılmıştır. Simülasyon deneyleri, meme içindeki tümör dokusunu modellemektedir. Her üç algoritma da tümör yüzeye yakınken gerçeğe daha yakın görüntüler üretmiştir. Tümörün meme yüzeyine yakın olmaması durumunda ise, Bi-CG ve SVD algoritmaları ile oluşturulan görüntülerdeki tümör konumu gerçek konumu değildir. Ancak TFQMR algoritması ile oluşturulan görüntüdeki tümör konumu, gerçek konumuna yakın elde edilmiştir. Geri çatım algoritmalarının sonuçları, Ortalama Yüzde Hata (MPE), Ortalama Kare Hata (MSE) ve Ortalama Mutlak Hata (MAE) metrikleri kullanılarak tümörlerin lokasyonunun doğru tanımlanmasına dayalı olarak değerlendirilmiştir. TFQMR algoritmasının DOT sistemleri için daha uygun bir geri çatım tekniği olduğu gösterilmiştir. Böylece, TFQMR'nin tıbbi görüntüleme sistemlerinde kullanılma potansiyeline sahip olabileceği sonucuna varıldı.

Anahtar Kelimeler

Geri Çatım Algoritması Tekil Değer Ayrışımı Bi-Konjuge Gradyan Transpozesiz Yarı Minimal Rezidüel

Kaynakça

  • [1] T. Mercan, G. Sevim, Y. A. Üncü, U. Serkan, H. Ö. Kazancı, and M. Canpolat, “The Comparison of Reconstruction Algorithms for Diffuse Optical Tomography,” Süleyman Demirel Üniversitesi Fen Edeb. Fakültesi Fen Derg., vol. 14, no. 2, pp. 285–295, 2019.
  • [2] G. Sevim, Y. A. Üncü, T. Mercan, and M. Canpolat, “Image reconstruction for diffuse optical tomography using bi-conjugate gradient and transpose-free quasi minimal residual algorithms and comparison of them,” Int. J. Imaging Syst. Technol., 1-12, Apr. 2021, doi: https://doi.org/10.1002/ima.22587.
  • [3] R. J. Gaudette et al., “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol., 45(4), 1051-70, Apr. 2000, doi: 10.1088/0031-9155/45/4/318.
  • [4] D. A. Boas et al., “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag., vol. 18, no. 6, pp. 57-75, Nov. 2001, doi: 10.1109/79.962278.
  • [5] R. W. Freund and N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math., 60, 315–339 (1991), doi: 10.1007/BF01385726.
  • [6] R. W. Freund, “A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems,” SIAM J. Sci. Comput., 14(2), 470-482, 1993, doi: 10.1137/0914029.
  • [7] R. E. Bank and T. F. Chan, “A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems,” Numer. Algorithms, 7(1), 1-16, 1994, doi: 10.1007/BF02141258.
  • [8] C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Clim. Res., vol. 30, no. 1, pp. 79–82, Dec. 2005, doi: 10.3354/CR030079.
  • [9] A. de Myttenaere, B. Golden, B. Le Grand, and F. Rossi, “Mean Absolute Percentage Error for regression models,” Neurocomputing, vol. 192, pp. 38–48, Jun. 2016, doi: 10.1016/J.NEUCOM.2015.12.114.
  • [10] Z. Wang and A. C. Bovik, “Mean squared error: Lot it or leave it? A new look at signal fidelity measures,” IEEE Signal Process. Mag., vol. 26, no. 1, pp. 98–117, 2009, doi: 10.1109/MSP.2008.930649.
  • [11] C. F. Van Loan, “Generalizing The Singular Value Decomposition.,” SIAM J. Numer. Anal., 13(1), 76-83, 1976, doi: 10.1137/0713009.
  • [12] V. C. Klema and A. J. Laub, “The Singular Value Decomposition: Its Computation and Some Applications,” IEEE Trans. Automat. Contr., 25(2), 164-176, 1980, doi: 10.1109/TAC.1980.1102314.
  • [13] S. L. Brunton and J. N. Kutz, “Chapter 1: Singular Value Decomposition (SVD),” in Data Driven Science & Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge, 3-47, 2019.
  • [14] C. Lanczos, “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators,” J. Res. Natl. Bur. Stand, 255-282, 1950, doi: 10.6028/jres.045.026.
  • [15] R. W. Freund, “Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems”, in Recent advances in iterative methods, Springer, New York, pp. 69–94, 1994.
  • [16] Y. A. Üncü, G. Sevim, and M. Canpolat, “Approaches to preclinical studies with heterogeneous breast phantom using reconstruction and three-dimensional image processing algorithms for diffuse optical imaging,” Int. J. Imaging Syst. Technol., Aug. 2021, doi: https://doi.org/10.1002/ima.22648.
  • [17] T. Mercan, G. Sevim, H. Ö. Kazancı, Y. A. Üncü, and M. Canpolat, “Comparison of images produced by diffuse optical tomography with two different backscatter techniques.” 2017 21st Natl. Biomed. Eng. Meet., (BIYOMUT), pp. i-iv, 2018, doi: 10.1109/BIYOMUT.2017.8479038.
  • [18] Y. A. Üncü, G. Sevim, T. Mercan, V. Vural, E. Durmaz, and M. Canpolat, “Differentiation of tumoral and non-tumoral breast lesions using back reflection diffuse optical tomography: A pilot clinical study,” Int. J. Imaging Syst. Technol., Apr. 2021, doi: https://doi.org/10.1002/ima.22578.
  • [19] G. Ortega, E. M. Garzón, F. Vázquez, and I. García, “The BiConjugate gradient method on GPUs,” 64(1), 49-58, 2013, doi: 10.1007/s11227-012-0761-2.
  • [20] R. W. Freund and N. M. Nachtigal, “An Implementation of the QMR Method Based on Coupled Two-Term Recurrences,” SIAM J. Sci. Comput., 5(2), 313-337, 1994, doi: 10.1137/0915022.

Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography

Yıl 2021, Cilt: 9 Sayı: 6 - ICAIAME 2021, 167 - 176, 31.12.2021

Gençay Sevim Yiğit Ali Üncü Murat Canpolat

https://doi.org/10.29130/dubited.1016284

Öz

In Diffuse Optical Tomography (DOT), data processing and reconstruction stages are crucial to obtain high-quality images. Thus, choosing suitable algorithms for the system is a critical choice. This study aims to determine an appropriate reconstruction algorithm for DOT imaging. There are several reconstruction algorithms used in DOT systems. Some algorithms have been improved for solving specific cases, and some still need to be improved. In this study, we used three algorithms for the reconstruction process: Singular Value Decomposition (SVD), Bi-Conjugated Gradient (Bi-CG), and Transpose Free Quasi Minimal Residual (TFQMR). In testing the algorithms, data of the simulation experiments have been used. The simulation experiments model the tumoral tissue within the breast. All three algorithms were produced correct images while the tumor close to the surface. In the case of the tumor that is not close to the breast surface, the tumor location on the images created by Bi-CG and SVD algorithms was not its actual location. However, the tumor location in the image created by the TFQMR algorithm was close to its actual location. Outcomes of the reconstruction algorithms were evaluated based on correctly defining the location of the tumors by using Mean Percentage Error (MPE), Mean Squared Error (MSE), and Mean Absolute Error (MAE) metrics. We have demonstrated the TFQMR algorithm is a more appropriate reconstruction technique for DOT systems. Thus, we have concluded that TFQMR can have the potential to be used in medical imaging systems.

Anahtar Kelimeler

Reconstruction Algorithm Singular Value Decomposition Bi-Conjugated Gradient Transpose Free Quasi Minimal Residual

Kaynakça

  • [1] T. Mercan, G. Sevim, Y. A. Üncü, U. Serkan, H. Ö. Kazancı, and M. Canpolat, “The Comparison of Reconstruction Algorithms for Diffuse Optical Tomography,” Süleyman Demirel Üniversitesi Fen Edeb. Fakültesi Fen Derg., vol. 14, no. 2, pp. 285–295, 2019.
  • [2] G. Sevim, Y. A. Üncü, T. Mercan, and M. Canpolat, “Image reconstruction for diffuse optical tomography using bi-conjugate gradient and transpose-free quasi minimal residual algorithms and comparison of them,” Int. J. Imaging Syst. Technol., 1-12, Apr. 2021, doi: https://doi.org/10.1002/ima.22587.
  • [3] R. J. Gaudette et al., “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol., 45(4), 1051-70, Apr. 2000, doi: 10.1088/0031-9155/45/4/318.
  • [4] D. A. Boas et al., “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag., vol. 18, no. 6, pp. 57-75, Nov. 2001, doi: 10.1109/79.962278.
  • [5] R. W. Freund and N. M. Nachtigal, “QMR: a quasi-minimal residual method for non-Hermitian linear systems,” Numer. Math., 60, 315–339 (1991), doi: 10.1007/BF01385726.
  • [6] R. W. Freund, “A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems,” SIAM J. Sci. Comput., 14(2), 470-482, 1993, doi: 10.1137/0914029.
  • [7] R. E. Bank and T. F. Chan, “A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems,” Numer. Algorithms, 7(1), 1-16, 1994, doi: 10.1007/BF02141258.
  • [8] C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Clim. Res., vol. 30, no. 1, pp. 79–82, Dec. 2005, doi: 10.3354/CR030079.
  • [9] A. de Myttenaere, B. Golden, B. Le Grand, and F. Rossi, “Mean Absolute Percentage Error for regression models,” Neurocomputing, vol. 192, pp. 38–48, Jun. 2016, doi: 10.1016/J.NEUCOM.2015.12.114.
  • [10] Z. Wang and A. C. Bovik, “Mean squared error: Lot it or leave it? A new look at signal fidelity measures,” IEEE Signal Process. Mag., vol. 26, no. 1, pp. 98–117, 2009, doi: 10.1109/MSP.2008.930649.
  • [11] C. F. Van Loan, “Generalizing The Singular Value Decomposition.,” SIAM J. Numer. Anal., 13(1), 76-83, 1976, doi: 10.1137/0713009.
  • [12] V. C. Klema and A. J. Laub, “The Singular Value Decomposition: Its Computation and Some Applications,” IEEE Trans. Automat. Contr., 25(2), 164-176, 1980, doi: 10.1109/TAC.1980.1102314.
  • [13] S. L. Brunton and J. N. Kutz, “Chapter 1: Singular Value Decomposition (SVD),” in Data Driven Science & Engineering: Machine Learning, Dynamical Systems, and Control, Cambridge, 3-47, 2019.
  • [14] C. Lanczos, “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators,” J. Res. Natl. Bur. Stand, 255-282, 1950, doi: 10.6028/jres.045.026.
  • [15] R. W. Freund, “Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems”, in Recent advances in iterative methods, Springer, New York, pp. 69–94, 1994.
  • [16] Y. A. Üncü, G. Sevim, and M. Canpolat, “Approaches to preclinical studies with heterogeneous breast phantom using reconstruction and three-dimensional image processing algorithms for diffuse optical imaging,” Int. J. Imaging Syst. Technol., Aug. 2021, doi: https://doi.org/10.1002/ima.22648.
  • [17] T. Mercan, G. Sevim, H. Ö. Kazancı, Y. A. Üncü, and M. Canpolat, “Comparison of images produced by diffuse optical tomography with two different backscatter techniques.” 2017 21st Natl. Biomed. Eng. Meet., (BIYOMUT), pp. i-iv, 2018, doi: 10.1109/BIYOMUT.2017.8479038.
  • [18] Y. A. Üncü, G. Sevim, T. Mercan, V. Vural, E. Durmaz, and M. Canpolat, “Differentiation of tumoral and non-tumoral breast lesions using back reflection diffuse optical tomography: A pilot clinical study,” Int. J. Imaging Syst. Technol., Apr. 2021, doi: https://doi.org/10.1002/ima.22578.
  • [19] G. Ortega, E. M. Garzón, F. Vázquez, and I. García, “The BiConjugate gradient method on GPUs,” 64(1), 49-58, 2013, doi: 10.1007/s11227-012-0761-2.
  • [20] R. W. Freund and N. M. Nachtigal, “An Implementation of the QMR Method Based on Coupled Two-Term Recurrences,” SIAM J. Sci. Comput., 5(2), 313-337, 1994, doi: 10.1137/0915022.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Gençay Sevim 0000-0002-2157-3209

Yiğit Ali Üncü 0000-0001-7398-9540

Murat Canpolat 0000-0003-3298-9725

Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 6 - ICAIAME 2021

Kaynak Göster

APA Sevim, G., Üncü, Y. A., & Canpolat, M. (2021). Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 9(6), 167-176. https://doi.org/10.29130/dubited.1016284
AMA Sevim G, Üncü YA, Canpolat M. Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography. DÜBİTED. Aralık 2021;9(6):167-176. doi:10.29130/dubited.1016284
Chicago Sevim, Gençay, Yiğit Ali Üncü, ve Murat Canpolat. “Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi 9, sy. 6 (Aralık 2021): 167-76. https://doi.org/10.29130/dubited.1016284.
EndNote Sevim G, Üncü YA, Canpolat M (01 Aralık 2021) Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 9 6 167–176.
IEEE G. Sevim, Y. A. Üncü, ve M. Canpolat, “Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography”, DÜBİTED, c. 9, sy. 6, ss. 167–176, 2021, doi: 10.29130/dubited.1016284.
ISNAD Sevim, Gençay vd. “Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography”. Düzce Üniversitesi Bilim ve Teknoloji Dergisi 9/6 (Aralık 2021), 167-176. https://doi.org/10.29130/dubited.1016284.
JAMA Sevim G, Üncü YA, Canpolat M. Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography. DÜBİTED. 2021;9:167–176.
MLA Sevim, Gençay vd. “Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography”. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, c. 9, sy. 6, 2021, ss. 167-76, doi:10.29130/dubited.1016284.
Vancouver Sevim G, Üncü YA, Canpolat M. Application of Reconstruction Algorithms by Simulation Experiments for the Diagnosis of Breast Tumor-Like Tissues Modeled in Diffuse Optical Tomography. DÜBİTED. 2021;9(6):167-76.
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