A technique based on Schur decomposition to supress the multiplicative (speckle) noise from medical ultrasound images is presented in this study. An image which carries the speckle noise is divided into small overlapping segments, size of these segments depends on the nature of speckle carried by the image and a global covariance matrix is calculated for the whole image by averaging the covariances of all segments. The global covariance matrix is decomposed through Schur decomposition to obtain the orthogonal vectors. A subset of these orthogonal vectors that correspond to largest magnitudes of eigenvalues are selected to filter out the speckle noise from the image. The proposed approach is compared with four benchmark filtering techniques, homomorphic wavelet despeckling, Wiener, Frost and Gamma. Two types of simulated ultrasound images and five types of real ultrasound images of foetal neck, left kidney, right kidney, musculo skeletal nerve and lymph node are tested. The proposed approach performed maximum suppression of speckle noise in all types of the images with optimal resolution and edge detection. The despeckling performance of the proposed approach is even better compared with the benchmark schemes once the speckle noise is rough, which is usually the case for soft tissue.

References

1. 1)
  - 14. Bakonyi, M., Constantinescu, T.: ‘Schur's algorithm and several applications’, Pitman Research Notes in Mathematics Series’ (Longman Scientific & Technical, Harlow, 1992), 261.
2. 2)
  - 17. Al-Asad, J.F., Reza, A.M., Techavipoo, U.: ‘An ultrasound image despeckling approach based on principle component analysis’, Int. J. Image Process. (IJIP), 2014, 8, (4), p. 156.
3. 3)
  - 16. Jain, A.K.: ‘Fundamentals of digital image processing’ (Prentice-Hall Inc., 1989).
4. 4)
  - 13. De Araujo, A.F., Constantinou, C.E., Tavares, J.M.R.: ‘Smoothing of ultrasound images using a new selective average filter’, Expert Syst. Appl., 2016, 60, pp. 96–106.
5. 5)
  - 5. Achim, A., Bezerianos, A., Tsakalides, P.: ‘Novel Bayesian multiscale method for speckle removal in medical ultrasound images’, IEEE Trans. Med. Imaging, 2001, 20, (8), pp. 772–783.
6. 6)
  - 20. Jensen, J.A.: ‘Field: a program for simulating ultrasound systems’. 10th Nordicbaltic Conf. on Biomedical Imaging, 1996, vol. 4, no. 1, pp. 351–353.
7. 7)
  - 12. Zhang, C., Wang, K.: ‘A switching median–mean filter for removal of high-density impulse noise from digital images’, Optik, Int. J. Light Electron Opt., 2015, 126, (9), pp. 956–961.
8. 8)
  - 18. Hao, X., Gao, S., Gao, X.: ‘A novel multiscale nonlinear thresholding method for ultrasonic speckle suppressing’, IEEE Trans. Med. Imaging, 1999, 18, (9), pp. 787–794.
9. 9)
  - 9. Nadernejad, E., Karami, M.R., Sharifzadeh, S., et al: ‘Despeckle filtering in medical ultrasound imaging’, Contemp. Eng. Sci., 2009, 2, (1), pp. 17–36.
10. 10)
  - 3. Goodman, J.W.: ‘Some fundamental properties of speckle’, J. Opt. Soc. Am., 1976, 66, pp. 1145–1150.
11. 11)
  - 10. Frost, V., Stiles, J., Shanmugan, K., et al: ‘A model for radar images and its application to adaptive digital filtering of multiplicative noise’, IEEE Trans. Pattern Anal. Mach. Intell., 1982, 2, pp. 157–165.
12. 12)
  - 22. Akansu, A.N., Haddad, R.A.: ‘Multiresolution signal decomposition: transforms, subbands, and wavelets’ (Academic Press, 2001).
13. 13)
  - 11. Saxena, N., Rathore, N.: ‘A review on speckle noise filtering techniques for SAR images’, Int. J. Adv. Res. Comput. Sci. Electron. Eng. (IJARCSEE), 2013, 2, (2), p. 243.
14. 14)
  - 4. Michailovich, O.V., Tannenbaum, A.: ‘Despeckling of medical ultrasound images’, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2006, 53, (1), pp. 64–78.
15. 15)
  - 7. Pratt, W.K.: ‘Generalized wiener filtering computation techniques’, IEEE Trans. Comput., 1972, 100, (7), pp. 636–641.
16. 16)
  - 21. Jensen, J.A., Svendsen, N.B.: ‘Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers’, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 1992, 39, (2), pp. 262–267.
17. 17)
  - 8. Gupta, S., Chauhan, R.C., Saxena, S.C.: ‘Homomorphic wavelet thresholding technique for denoising medical ultrasound images’, J. Med. Eng. Technol., 2005, 29, (5), pp. 208–214.
18. 18)
  - 6. Odegard, J.E., Guo, H., Burrus, C.S., et al: ‘Joint compression and speckle reduction of SAR images using embedded zero-tree models’. Proc. Workshop Image and Multidimensional Signal Processing, Belize City, Belize, March 1996, pp. 3–6.
19. 19)
  - 23. ‘Database of ultrasound images’. Available at http://www.ultrasound-images.com/.
20. 20)
  - 2. Chapman, A., Ter Haar, G.: ‘Thermal ablation of uterine fibroids using MR-guided focused ultrasound-a truly non-invasive treatment modality’, Eur. Radiol., 2007, 17, (10), pp. 2505–2511.
21. 21)
  - 15. Lund, J., Bowers, K.L.: ‘Sinc methods for quadrature and differential equations’ (Society for Industrial and Applied Mathematics, 1992).
22. 22)
  - 1. Fenster, A., Downey, D.B., Cardinal, H.N.: ‘Three-dimensional ultrasound imaging’, Phys. Med. Biol., 2001, 46, (5), pp. 67–99.
23. 23)
  - 19. Salinas, H.M., Fernández, D.C.: ‘Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography’, IEEE Trans. Med. Imaging, 2007, 26, (6), pp. 761–771.

Speckle suppression in medical ultrasound images through Schur decomposition

References

Related content