A good statistical model is necessary for the reduction in speckle noise. The Nakagami model is more general than the Rayleigh distribution for statistical modeling of speckle in ultrasound images. In this article, the Nakagami-based noise removal method is presented to enhance thyroid ultrasound images and to improve clinical diagnosis. The statistics of log-compressed image are derived from the Nakagami distribution following a maximum a posteriori estimation framework. The minimization problem is solved by optimizing an augmented Lagrange and Chambolle’s projection method. The proposed method is evaluated on both artificial speckle-simulated and real ultrasound images. The experimental findings reveal the superiority of the proposed method both quantitatively and qualitatively in comparison with other speckle reduction methods reported in the literature. The proposed method yields an average signal-to-noise ratio gain of more than 2.16 dB over the non-convex regularizer-based speckle noise removal method, 3.83 dB over the Aubert–Aujol model, 1.71 dB over the Shi–Osher model and 3.21 dB over the Rudin–Lions–Osher model on speckle-simulated synthetic images. Furthermore, visual evaluation of the despeckled images shows that the proposed method suppresses speckle noise well while preserving the textures and fine details.
DuttVGreenleafJF. Adaptive speckle reduction filters for log-compressed B-scan images. IEEE T Med Imaging1996; 15: 802–813.
2.
HaoXGaoSGaoX. A novel multiscale nonlinear thresholding method for ultrasonic speckle suppressing. IEEE T Med Imaging1999; 18: 787–794.
3.
HealyAJLeenmanS. Speckle reduction methods in ultrasound pulse echo imaging. In: International conference on acoustic sensing and imaging, London, 29–30 March 1993, pp. 68–76. New York: IEEE.
4.
ShankarPM. Ultrasonic tissue characterization using a generalized Nakagami model. IEEE T Ultrason Ferr2001; 48: 1716–1720.
5.
RangrazPBehnamHTavakkoliJ. Nakagami imaging for detecting thermal lesions induced by high-intensity focused ultrasound in tissue. Proc IMechE, Part H: J Engineering in Medicine2014; 228(1): 19–26.
6.
GuptaSKaurLChauhanRC. Robust non-homomorphic approach for speckle reduction in medical ultrasound images. Med Biol Eng Comput2005; 43: 189–195.
7.
EltoftT. Modeling the amplitude statistics of ultrasonic images. IEEE T Med Imaging2006; 25: 229–240.
8.
KolarRJanhJ. Tissue models and speckle reduction in medical ultrasound images. In: KalviainenHParkkinenJKaarnaA (eds) Image analysis: Scandinavian conference on image analysis (Lecture Notes in Computer Science, vol. 3540). Berlin; Heidelberg: Springer-Verlag, 2005, pp.1017–1026.
9.
GhofraniSJahed-MotlaghMRAyatollahiA. An adaptive speckle suppression filter based on Nakagami distribution. In: IEEE international conference on trends in communications, Bratislava, 4–7 July 2001, vol. 1, pp.84–87. New York: IEEE.
10.
ChanTFShenJVeseL. Variational PDE models in image processing. Not AMS2002; 50: 14–26.
11.
Li-LiHXiaoLWeiZ. Multiplicative noise removal via a novel variational model. Int J Image Video Process2010; 1–16.
12.
RudinLLionsPLOsherS. Multiplicative denoising and deblurring: theory and algorithms. In: OsherSParagiosN (eds) Geometric level sets in imaging, vision, and graphics. Berlin: Springer, 2003, pp.103–119.
13.
AubertGAujolJF. A variational approach to remove multiplicative noise. SIAM J Appl Math2003; 68: 925–946.
14.
ShiJOsherS. A nonlinear inverse scale space method for a convex multiplicative noise model. SIAM J Appl Math2008; 1: 294–321.
15.
HuangYNgMKWenY. A new total variation method for multiplicative noise removal. SIAM J Imaging Sci2009; 2: 20–40.
16.
Bioucas-DiasJFigueiredoM. Multiplicative noise removal using variable splitting and constrained optimization. IEEE Transactions on Image Processing2010; 19: 1720–1730.
17.
SteidlGTeuberT. Removing multiplicative noise by Douglas–Rachford splitting methods. J Math Imag Vis2010; 36: 168–184.
18.
ZhangHYPengQC. Adaptive image denoising model based on total variation. Opto Electron Eng2006; 33: 50–53.
BuadesACollBMorelJM. A non-local algorithm for image denoising. In: IEEE computer society conference on computer vision and pattern recognition, Genoa, 11–14 September 2005, vol. 2, pp.60–65. New York: IEEE.
30.
GuptaSKaurLChauhanRC. A verastile technique for visual enhancement of medical ultrasound images. Digital Signal Process2007; 17: 542–560.
31.
ZhangLZhangDMouX. FSIM: a Feature similarity index for image quality assessment. IEEE T Image Process2011; 20: 2378–2386.
32.
SheikhHRBovikAC. Image information and visual quality image processing. IEEE T Image Process2006; 15: 430–444.
33.
WangZBovikAC. A universal image quality index. IEEE Signal Proc Let2002; 9: 81–84.
34.
SattarFFlorebyLSalomonssonG. Image enhancement based on a nonlinear multiscale method. IEEE T Image Process1997; 6: 888–895.
35.
WangZSimoncelliEPBovikAC. Multi-scale structural similarity for image quality assessment. In: IEEE asilomar conference on signals, systems and computers, Pacific Grove, CA, 9–12 November 2003, vol. 2, pp.1398–1402. New York: IEEE.
36.
CoupePHellierPKervrannC. Bayesian non local means-based speckle filtering. IEEE T Med Imaging2008; 1: 1291–1294.
37.
GoldsteinTOsherS. The split Bregman method for l1-regularized problems. SIAM J Imaging Sci2009; 2: 323–343.
38.
JensenJA. Simulation of advanced ultrasound systems using field II. In: IEEE international symposium on biomedical imaging: nano to macro, Arlington, VA, 15–18 April 2004, pp.636–639. New York: IEEE.
