# Speckle Reduction on Ultrasound Liver Images Based on a Sparse Representation over a Learned Dictionary

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Ultrasound Noise Model

#### 2.2. Related Work on Multiplicative Noise Reduction

_{c}columns of N

_{r}elements, is called a sparse-land model [36]. K-singular value decomposition seeks the best signal representation of image signal y from the sparsest representation $\alpha $:

## 3. Sparse Representation Framework for Speckle Reduction

_{0}is the cut-off frequency and f is the order of the filter. We varied the frequency values u and v of the i and j spatial coordinates. We used the BW-HP filter because it generates fewer ringing artifacts on the image signal.

- Convert the multiplicative noise into additive noise using an enhanced homomorphic filter and capture the high- and low-frequency components to retain detailed information.
- Apply pixel-based TV regularization to smooth the filtered image signal.
- Apply patch-based sparse representation over a dictionary trained using the KSVD algorithm. We employed two modified dictionaries—one trained with a set of reference ultrasound image patches and another trained using the speckled image patches.
- Iterate between the TV regularization and sparse representation procedure to improve the reconstructed image.

#### 3.1. Performance Estimation

_{max}represents the maximum fluctuations in the input image. Here, N

_{max}= (2

^{n}− 1), N

_{max}= 255, when the components of a pixel are encoded using eight bits. N denotes the number of pixels processed, $x(n,m)$ is the original signal, and $\stackrel{\u2322}{x}(n,m)$ is the recovered image signal. In MSSIM, the structures of the two images are compared after normalizing the variance and subtracting the luminance as follows:

## 4. Experimental Results and Discussion

#### 4.1. Simulations on Synthetic Images

#### 4.2. Clinical Liver Ultrasound Images

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Szabo, T.L. Diagnostic Ultrasound Imaging: Inside Out; Academic Press Series in Biomedical Engineering; Elsevier Academic Press: New York, NY, USA, 2004; p. 549. ISBN 0-12-680145-2. [Google Scholar]
- Martial, B.; Cachar, D. Acquire real-time RF digital ultrasound data from a commercial scanner. Electron. J. Tech. Accoust.
**2007**, 3, 16. [Google Scholar] - Lee, H.; Chen, Y.P.P. Image based computer aided diagnosis system for cancer detection. Expert Syst. Appl.
**2015**, 42, 5356–5365. [Google Scholar] [CrossRef] - Jabarulla, M.Y.; Lee, H.N. Computer aided diagnostic system for ultrasound liver images: A systematic review. Optik
**2017**, 140, 1114–1126. [Google Scholar] [CrossRef] - Zanotel, M.; Bednarova, I.; Londero, V.; Linda, A.; Lorenzon, M.; Girometti, R.; Zuiani, C. Automated breast ultrasound: Basic principles and emerging clinical applications. Radiol. Med.
**2018**, 123, 1–12. [Google Scholar] [CrossRef] [PubMed] - Acharya, U.R.; Koh, J.E.W.; Hagiwara, Y.; Tan, J.H.; Gertych, A.; Vijayananthan, A.; Yaakup, N.A.; Abdullah, B.J.J.; Fabell, M.K.B.M.; Yeong, C.H. Automated diagnosis of focal liver lesions using bidirectional empirical mode decomposition features. Comput. Biol. Med.
**2017**, 94, 11–18. [Google Scholar] [CrossRef] [PubMed] - Grazioli, L.; Ambrosini, R.; Frittoli, B.; Grazioli, M.; Morone, M. Primary benign liver lesions: Benign focal liver lesions can origin from all kind of liver cells: Hepatocytes, mesenchymal and cholangiocellular line. Eur. J. Radiol.
**2017**, 26, 378–398. [Google Scholar] [CrossRef] [PubMed] - Burckhart, C.B. Speckle in ultrasound B-mode scans. IEEE Trans. Sonics Ultrason.
**1978**, 25, 1–6. [Google Scholar] [CrossRef] - Narayanan, S. A view on despeckling in ultrasound imaging. Int. J. Signal Process. Image Process. Pattern Recognit.
**2009**, 2, 85–98. [Google Scholar] - Lopes, A.; Touzi, R.; Nezry, E. Adaptive Speckle Filters and Scene Heterogeneity. IEEE Trans. Geosci. Remote Sens.
**1990**, 28, 992–1000. [Google Scholar] [CrossRef] - Lee, J.S. Digital image enhancement and noise filtering by use of local statistics. IEEE Trans. Pattern Anal. Mach. Intell.
**1980**, 2, 165–168. [Google Scholar] [CrossRef] [PubMed] - Gonzalez, R.C.; Woods, R.E. Digital Image Processing, 3rd ed.; Pearson Education, Inc.: London, UK, 2008; ISBN 0-13-168728-x978-0-13-168728-8. [Google Scholar]
- Goldstein, J.S.; Reed, I.S.; Scharf, L.L. A multistage representation of the Wiener filter based on orthogonal projections. IEEE Trans. Inf. Theory
**1998**, 44, 2943–2959. [Google Scholar] [CrossRef] - Kuan, D.T.; Sawchuk, A.A.; Strand, T.C.; Chavel, P. Adaptive noise smoothing filter for images with signal-dependent noise. IEEE Trans. Pattern Anal. Mach. Intell.
**1985**, 7, 165–177. [Google Scholar] [CrossRef] [PubMed] - Simon, P.; Patrick, H. Median Filtering in Constant Time. IEEE Trans. Image Process.
**2007**, 16, 2389–2394. [Google Scholar] - Achim, A.; Bezerianos, A.; Tsakalides, P. Novel Bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Trans. Med. Imaging
**2001**, 20, 772–783. [Google Scholar] [CrossRef] [PubMed] - Chen, Z.J.; Chen, C.H.Y. Efficient statistical modeling of wavelet coefficients for image denoising. Int. J. Wavelets Multiresolut. Inf. Process.
**2009**, 7, 629–641. [Google Scholar] [CrossRef] - Vishwa, A.; Sharma, S. Modified method for denoising the ultrasound images by wavelet thresholding. Int. J. Intell. Syst. Appl.
**2012**, 4, 25. [Google Scholar] [CrossRef] - Shen, Y.; Liu, Q.; Lou, S.; Hou, Y.L. Wavelet-Based Total Variation and Nonlocal Similarity Model for Image Denoising. IEEE Signal Process. Lett.
**2017**, 24, 877–881. [Google Scholar] [CrossRef] - Donoho, D.L. De-noising by soft-thresholding. IEEE Trans. Inf. Theory
**1995**, 41, 613–627. [Google Scholar] [CrossRef] - Matsuyama, E.; Tsai, D.-Y.; Lee, Y.; Tsurumaki, M.; Takahashi, N.; Watanabe, H.; Chen, H.-M. A modified undecimated discrete wavelet transform based approach to mammographic image denoising. J. Digit. Imaging
**2013**, 26, 748–758. [Google Scholar] [CrossRef] [PubMed] - Kim, Y.S. Improvement of ultrasound image based on wavelet transform: Speckle reduction and edge enhancement. SPIE Med. Imaging
**2005**, 5747, 1085–1092. [Google Scholar] - Chambolle, A. An algorithm for total variation minimizations and applications. J. Math. Imaging Vis.
**2004**, 10, 89–97. [Google Scholar] - Rudin, L.I.; Osher, S.; Fatemi, E. Nonlinear total variation based noise removal algorithms. Phys. D Nonlinear Phenom.
**1992**, 60, 259–268. [Google Scholar] [CrossRef] - Perona, P.; Malik, J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell.
**1990**, 12, 629–639. [Google Scholar] [CrossRef] - Chao, S.M.; Tsai, D.M. An improved anisotropic diffusion model for detail and edge-preserving smoothing. Pattern Recognit. Lett.
**2010**, 31, 2012–2023. [Google Scholar] [CrossRef] - Tschumperle, D.; Deriche, R. Vector-valued image regularization with PDEs: A common framework for different applications. IEEE Trans. Pattern Anal. Mach. Intell.
**2005**, 27, 506–517. [Google Scholar] [CrossRef] [PubMed] - Zhao, Y.; Yang, J. Hyperspectral image denoising via sparse representation and low-rank constraint. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 296–308. [Google Scholar] [CrossRef] - Elad, M.; Aharon, M. Image denoising via sparse and redundant representations over learned dictionaries in wavelet domain. IEEE Trans. Image Process.
**2006**, 15, 754–758. [Google Scholar] [CrossRef] - Deka, B.; Bora, P.K. Removal of correlated speckle noise using sparse and overcomplete representations. Biomed. Signal Process. Control
**2013**, 8, 520–533. [Google Scholar] [CrossRef] - Fan, J.; Wu, Y.; Li, M.; Liang, W.; Zhang, Q. SAR Image Registration Using Multiscale Image Patch Features with Sparse Representation. Biomed. Signal Process. Control
**2017**, 10, 1483–1493. [Google Scholar] [CrossRef] - Wright, J.; Ma, Y.; Mairal, J.; Sapiro, G.; Huang, T.S.; Yan, S. Sparse representation for computer vision and pattern recognition. Proc. IEEE
**2010**, 98, 1031–1044. [Google Scholar] [CrossRef] - Bruckstein, M.E.A.M.; Donoho, D.L.; Elad, M. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev.
**2009**, 51, 34–81. [Google Scholar] [CrossRef] - Li, S.; Wang, G.; Zhao, X. Multiplicative noise removal via adaptive learned dictionaries and TV regularization. Digit. Signal Process.
**2016**, 50, 218–228. [Google Scholar] - Liu, K.; Tan, J.; Su, B. An Adaptive Image Denoising Model Based on Tikhonov and TV Regularizations. Adv. Multimed.
**2014**, 2014, 934834. [Google Scholar] [CrossRef] - Aharon, M.; Elad, M.; Bruckstein, A.M. The K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representations. IEEE Trans. Signal Process.
**2006**, 54, 4311–4322. [Google Scholar] [CrossRef] - Tay, P.C.; Garson, C.D.; Acton, S.T.; Hossack, J.A. Ultrasound despeckling for contrast enhancement. IEEE Trans. Image Process.
**2010**, 19, 1847–1860. [Google Scholar] [CrossRef] [PubMed] - Joel, T.; Sivakumar, R. An extensive review on Despeckling of medical ultrasound images using various transformation techniques. Appl. Acoust.
**2018**, 138, 18–27. [Google Scholar] [CrossRef] - Youngjian, Y.; Acton, S.T. Speckle reducing anisotropic diffusion. IEEE Trans. Image Process.
**2002**, 11, 1260–1270. [Google Scholar] [CrossRef] [PubMed] - Hussain, S.A.; Gorashi, S.M. Image Denoising based on Spatial/Wavelet Filter using Hybrid Thresholding Function. Int. J. Comput. Appl.
**2012**, 42, 5–13. [Google Scholar] - Aubert, G.; Aujol, J.-F. A variational approach to removing multiplicative noise. SIAM J. Appl. Math.
**2008**, 68, 925–946. [Google Scholar] [CrossRef] - Buades, A.; Coll, B.; Morel, J.M. A review of image denoising algorithms, with a new one. Multiscale Model. Simul.
**2005**, 4, 490–530. [Google Scholar] [CrossRef] - Gilboa, S.O.G. Nonlocal operators with applications to image processing. SIAM J. Multiscale Model. Simul.
**2008**, 7, 1005–1028. [Google Scholar] [CrossRef] - Cai, T.T.; Wang, L. Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans. Inf. Theory
**2011**, 57, 4680–4688. [Google Scholar] [CrossRef] - Deka, B.; Bora, P.K. Despeckling of medical ultrasound images using sparse representation. In Proceedings of the 2010 International Conference Signal Processing and Communications (SPCOM), Bangalore, India, 18–21 July 2010. ISSN 2165-0608. [Google Scholar]
- Cobbold, R.S.C. Foundations of Biomedical Ultrasound; Oxford University Press: Oxford, UK, 2007. [Google Scholar]
- Yahya, N.; Kamel, N.S.; Malik, A.S. Subspace-based technique for speckle noise reduction in ultrasound images. Biomed. Eng. Online
**2014**, 13, 154. [Google Scholar] [CrossRef] [PubMed] - Arsenault, H.H.; Levesque, M. Combined homomorphic and local-statistics processing for restoration of images degraded by signal-dependent noise. Appl. Opt.
**1984**, 23, 845–850. [Google Scholar] [CrossRef] [PubMed] - Xie, H.; Pierce, L.E.; Ulaby, F.T. Statistical properties of logarithmically transformed speckle. IEEE Trans. Geosci. Remote Sens.
**2002**, 40, 721–727. [Google Scholar] [CrossRef] - Candes, E.; Candes, E.; Romberg, J.; Romberg, J. l1-Magic: Recovery of Sparse Signals via Convex Programming; Caltech: Pasadena, CA, USA, 2005; pp. 1–19. [Google Scholar]
- Afonso, M.V.; Bioucas-Dias, J.M.; Figueiredo, M.A.T. An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process.
**2011**, 20, 681–695. [Google Scholar] [CrossRef] [PubMed] - Davis, G.; Mallat, S.G.; Avellaneda, M. Adaptive greedy approximations. Constr. Approx.
**1997**, 13, 57–98. [Google Scholar] [CrossRef] - Xiang, F.; Wang, Z. Split Bregman iteration solution for sparse optimization in image restoration. Optik
**2014**, 125, 5635–5640. [Google Scholar] [CrossRef] - Wang, Z.; Bovik, A.; Sheikh, H.; Simoncelli, E. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process.
**2004**, 4, 600–612. [Google Scholar] [CrossRef] - Shepp, L.; Logan, F. The Fourier reconstruction of a head section. IEEE Trans. Nucl. Sci.
**1974**, 21, 21–43. [Google Scholar] [CrossRef] - Llach, F. Hypercoagulability, renal vein thrombosis, and other thrombotic complications of nephrotic syndrome. Kidney Int.
**1985**, 3, 429–439. [Google Scholar] [CrossRef] - GitHub. Available online: https://github.com/sfikas/medical-imaging-datasets (accessed on 1 May 2018).

**Figure 1.**Flow diagram of the enhanced homomorphic filter. FFT: fast Fourier transform; IFFT inverse fast Fourier transform.

**Figure 2.**(

**a**) Noisy ultrasound image; (

**b**) Butterworth high-pass (BW-HP) filtered image; (

**c**) Gaussian low pass (GLP) filtered image; and (

**d**) transformed output of ultrasound noisy image.

**Figure 4.**(

**a**) Original image; (

**b**) noisy image. Results of the proposed method with (

**c**) Dictionary 1 and (

**d**) Dictionary 2; Results of the (

**e**) Frost; (

**f**) wavelet; (

**g**) Kuan; (

**h**) median; (

**i**) Weiner; and (

**j**) speckle reducing anisotropic diffusion (SRAD) filters.

**Figure 5.**The random collections of 16 × 16 atoms (K = 256) of trained dictionary from (

**a**) a reference set of 3245 ultrasound images and (

**b**) a noisy image.

**Figure 6.**Reconstruction of liver right lobe images. (

**a**) Original ultrasound image; (

**b**) Speckled ultrasound image (PSNR = 28.148 dB); Images reconstructed using (

**c**) Dictionary 1 (PSNR = 35.033 dB) and (

**d**) Dictionary 2 (PSNR = 35.537 dB).

**Figure 7.**Despeckled results obtained for the ultrasound liver dataset using a linear transducer with a frequency of 8 MHz. The red and the green boxes highlight the differences observed from the noisy and filtered images. (

**a**) Speckled image and results yielded by the proposed method using (

**b**) Dictionary 1 and (

**c**) Dictionary 2 as well as results using the (

**d**) Frost; (

**e**) median; (

**f**) Kuan; (

**g**) wavelet; (

**h**) Weiner; and (

**i**) SRAD filters.

**Figure 8.**Comparison of PSNRs obtained by different methods. SRAD: speckle reducing anisotropic diffusion.

**Figure 9.**(

**a**) Ultrasound image of the thrombus in the left ventricle. LV: left ventricle, RA: right atrium and RV: right ventricle and (

**b**) noisy image. Despeckled ultrasound images of proposed method using (

**c**) Dictionary 1 and (

**d**) Dictionary 2. Results using the (

**e**) Frost, (

**f**) median, (

**g**) Kuan, (

**h**) wavelet, (

**i**) Weiner, and (

**j**) SRAD filters. The dashed white box indicates the region of image showing visual enhancement owing to despeckling.

**Figure 10.**(

**a**) Zoomed sub-image of noisy thrombus ultrasound images. The red boxes highlight texture details of images for visual assessment. Results of proposed method using (

**b**) Dictionary 1 and (

**c**) Dictionary 2. Results using the (

**d**) Frost; (

**e**) median; (

**f**) Kuan; (

**g**) wavelet; (

**h**) Weiner; and (

**i**) SRAD filters.

**Table 1.**Peak signal-to-noise ratio (PSNR) and mean structural similarity (MSSIM) for the synthetic images for $\sigma $ = 10.

Models | PSNR (dB) | MSSIM |
---|---|---|

Noise image | 32.113 | 0.727 |

Frost | 32.466 | 0.768 |

Wavelet | 33.214 | 0.801 |

Kuan | 32.895 | 0.794 |

Median | 34.597 | 0.839 |

SRAD | 33.434 | 0.827 |

Weiner | 33.782 | 0.834 |

Proposed: Dictionary 1 | 36.862 | 0.953 |

Proposed: Dictionary 2 | 37.044 | 0.967 |

Models | PSNR (dB) | MSSIM |
---|---|---|

Frost | 28.966 | 0.822 |

Median | 25.497 | 0.659 |

Wavelet | 27.772 | 0.782 |

SRAD | 28.766 | 0.813 |

Kuan | 28.279 | 0.801 |

Weiner | 29.218 | 0.834 |

Proposed: Dictionary 1 | 30.334 | 0.901 |

Proposed: Dictionary 2 | 30.807 | 0.926 |

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**MDPI and ACS Style**

Jabarulla, M.Y.; Lee, H.-N. Speckle Reduction on Ultrasound Liver Images Based on a Sparse Representation over a Learned Dictionary. *Appl. Sci.* **2018**, *8*, 903.
https://doi.org/10.3390/app8060903

**AMA Style**

Jabarulla MY, Lee H-N. Speckle Reduction on Ultrasound Liver Images Based on a Sparse Representation over a Learned Dictionary. *Applied Sciences*. 2018; 8(6):903.
https://doi.org/10.3390/app8060903

**Chicago/Turabian Style**

Jabarulla, Mohamed Yaseen, and Heung-No Lee. 2018. "Speckle Reduction on Ultrasound Liver Images Based on a Sparse Representation over a Learned Dictionary" *Applied Sciences* 8, no. 6: 903.
https://doi.org/10.3390/app8060903