Abstract
Speckle noise of ultrasound images is of multiplicative nature which degrades the image quality in terms of resolution and contrast. While there exist a number of algorithms for reduction of multiplicative Rayleigh distributed random speckle noise, the low signal-to-noise ratio (SNR) issue of the multiplicative Rayleigh noise is still not adequately resolved. In this paper, a simple 2-dimensional (2D) local intensity smoothing method is presented which transforms the Rayleigh noise contaminated in ultrasound images to Nakagami distributed noise so as to improve the SNR of processed images. A 2D total variation regularized Nakagami speckle reduction algorithm is derived based on the maximum a posteriori estimation framework, which performs well in restoring piecewise-smooth reflectivity and preserving fine details of the image. The proposed algorithm is verified by a series of computer-simulated and real ultrasound image data. It is shown that the algorithm considerably improves the quality of ultrasound images and outperforms the Rayleigh noise based speckle reduction methods in terms of speckle SNR and contrast-to-noise ratio.
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References
Aubert G., Aujol J.-F. (2008) A variational approach to removing multiplicative noise. SIAM Journal on Applied Mathematics 68(4): 925–946
Aysal T. C., Barner K. E. (2007) Rayleigh-maximum-likelihood filtering for speckle reduction of ultrasound images. IEEE Transactions on Medical Imaging 26: 712–727
Bioucas-Dias J. M., Figueiredo M. A. T. (2010) Multiplicative noise removal using variable splitting and constrained optimization. IEEE Transactions on Image Processing 19: 1720–1730
Boyd S., Vandenberghe L. (2004) Convex optimization. Cambridge University Press, Cambridge
Candes E., Romberg J., Tao T. (2006) Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics 59: 1207–1223
Chambolle A. (2004) An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20: 89–97
Cincotti G., Loi G., Pappalardo M. (2001) Frequency decomposition and compounding of ultrasound medical images with wavelet packets. IEEE Transactions on Medical Imaging 20: 764–771
Eltoft T. (2006) Modeling the amplitude statistics of ultrasonic images. IEEE Transactions on Medical Imaging 25: 229–240
Goodman J. W. (2007) Speckle phenomena in optics: Theory and applications. Roberts & Company, Englewood, Colorado
Huang Y., Ng M. K., Wen Y. (2009) A new total variation method for multiplicative noise removal. SIAM Journal on Imaging Sciences 2(1): 20–40
Jablonski B. (2008) Anisotropic filtering of multidimensional rotational trajectories as a generalization of 2D diffusion process. Multidimensional Systems and Signal Processing 19: 379–399
Krishnamoorthy K. (2006) Handbook of statistical distributions with applications. Chapman & Hall/CRC, London
Li S. Z. (2009) Markov random field modeling in image analysis. Springer, Berlin
Li, R., Sun, Z., & Zhang, C. (2008). Adaptive filter for speckle reduction with feature preservation in medical ultrasound images. In 10th international conference on control automation robotics and vision (pp. 1787–1792).
Lin, Z., Chen, M., & Ma, Y. (2009). The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrix. Technical report UILU-ENG-09-2215.
Lopes, A., Nezry, E., Touzi, R., & Laur, H. (1990). Maximum a posteriori speckle filtering and first order texture models in SAR images. In 10th annual international geoscience and remote sensing symposium (pp. 2409–2412).
Nakagami M. (1960) The M-distribution—a general formula of intensity distribution of rapid fading. Statistical Method of Radio Propagation 21(7): 1157–1159
Ng M., Wang F., Yuan X.-M. (2011) Fast minimization methods for solving constrained total-variation superresolution image reconstruction. Multidimensional Systems and Signal Processing 22: 259–286
Ng M., Yip A. (2001) A fast MAP algorithm for high-resolution image reconstruction with multisensors. Multidimensional Systems and Signal Processing 12: 143–164
Park, J., Song, W., & Pearlman, W. (1999). Speckle filtering of SAR images based on adaptive windowing. In IEE proceedings—vision image and signal processing (Vol. 146, pp. 191–197).
Rabal, H. J. & Braga, R. A. Jr. (2009). Dynamic laser speckle and applications. CRC press, Boca Raton, FL.
Shankar P. (2000) A general statistical model for ultrasonic backscattering from tissues. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 47: 727–736
Tur M., Chin K. C., Goodman J. W. (1982) When is speckle noise multiplicative?. Applied Optics 21(7): 1157–1159
Wang Y., Yang J., Yin W., Zhang Y. (2008) A new alternating minimization algorithm for total variation image reconstruction. SIAM Journal on Imaging Sciences 1(3): 248–272
Yu, C., Zhang, C., & Xie, L. (2012) An envelope signal based deconvolution algorithm for ultrasound imaging. In Signal processing (Vol. 92, pp. 793–800) (To appear).
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Yu, C., Zhang, C. & Xie, L. A multiplicative Nakagami speckle reduction algorithm for ultrasound images. Multidim Syst Sign Process 23, 499–513 (2012). https://doi.org/10.1007/s11045-012-0173-8
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DOI: https://doi.org/10.1007/s11045-012-0173-8