Research on Biomedical Engineering
Research on Biomedical Engineering
Original article

Mean scatterer space estimation from ultrasound signals combining singular spectral analysis and entropy

Adriana Kauati, Wagner Coelho de Albuquerque Pereira, Marcello Luiz Rodrigues Campos


Introduction: Ultrasound (US) is a nonionizing radiation capable of real time imaging at low cost. Its most attractive application is quantitative tissue characterization with the objective of differentiating normal tissues from diseased tissues. In this study, an automated method using singular spectrum analysis (SSA) to estimate the mean scatterer space (MSS) of US signals is proposed.

Methods: Entropy was used to determine the optimal number of components for the SSA. Subsequently, this number was compared with the results using a fixed number of
components. A method based on the spectrum of the original signal was also used for comparison. The method was evaluated by using 24,000 simulated US signals, i.e., echoes and jitters backscattered from samples with different ratios of regular-to-irregular structure, as well as with 152 signals obtained from a phantom made of nylon wires.

Results: For the simulated signals, the proposed method for estimating the MSS presented results similar to the other methods that were tested. However, the magnitude-of-the-spectrum method loses the phase information, and hence, does not allow the characterization of irregular structures. For the signals recorded from the phantom, the methods using SSA and entropy achieved better results.

Conclusion: In this study, the combination of SSA with entropy to estimate the MSS of a periodic or quasi‑periodic medium was proposed. The proposed method achieved similar or better results compared with two other methods found in the scientific literature. The novelty of the proposed method is the application of entropy as a quantitative criterion for selecting the SSA periodic components, allowing it to become independent of heuristic criteria.


Ultrasound, Tissue characterization, Singular spectral analysis, Entropy, Mean space scatterer


Bridal SL, Saïed A, Chérin E, Lefèbvre F, Laugier P, Berger G. High-resolution quantitative echography with tissue parameters. JEMU. 1998; 19(2-3):204-11.

Chen SP, Tsao S, Tsao J. A joint time-frequency approach to mean scatterer spacing estimation. In: Ding Y, Peng, Y, Shi R, Hao K, Wang L, editors. Proceedings of the 2011 4th International Conference on Biomedical Engineering and Informatics (BMEI 2011); 2011 Oct 15-17; Shangai, China. USA: IEEE; 2011. p. 602-6.

Cover TM, Thomas JA. Elements of information theory. USA: Wiley-Interscience; 1991.

Donohue KD, Huang L, Burks T, Forsberg F, Piccoli CW. Tissue classification with generalized spectrum parameters. Ultrasound Med Biol. 2001; 27(11):1505-14. PMid:11750750.

Huang L, Donohue KD, Genis V, Forsberg F. Duct detection and wall spacing estimation in breast tissue. Ultrason Imaging. 2000; 22(3):137-52. PMid:11297148.

Kauati A, Pereira WCA, Campos MLRC. Detecção automática do espaçamento médio de meios periódicos por sinais ultrassônicos retroespalhados. Rev Bras Eng Bioméd. 2012; 28(3):261-71.

Pan W, Shen Y, Liu T, Wang Y. Mode Decomposition based cepstrum measurement of scatterer Spacing with Ultrasonic Scattering. In: Li J, editor. Proceedings of the 2014 Fourth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC 2014); 2014 Sept 18-20; Harbin, Heilongjiang, China. USA: IEEE; 2014. p. 412-7.

Pan W, Shen Y, Liu T, Wang Y. Golay improvement of the robustness of mean scatterer spacing measurement with ultrasonic backscattering. Biomed Mater Eng. 2015; 26(1):455-65. PMid:26406037.

Pereira WCA, Abdelwahab A, Bridal SL, Laugier P. Singular spectrum analysis applied to 20MHz backscattered ultrasound signals from periodic and quasi-periodic phantoms. Acoust Imag. 2002; 26:239-46.

Pereira WCA, Bridal SL, Coron A, Laugier P. Singular spectrum analysis applied to backscattered ultrasound signals from in vitro human cancellous bone specimens. IEEE Trans Ultrason Ferroelectr Freq Control. 2004; 51(3):302-12. PMid:15128217.

Pereira WCA, Maciel CD. Performance of ultrasound echo decomposition using singular spectrum analysis. Ultrasound Med Biol. 2001; 27(9):1231-8. PMid:11597364.

Rubert N, Varghese T. Mean scatterer spacing estimation using multi-taper coherence. IEEE Trans Ultrason Ferroelectr Freq Control. 2013; 60(6):1061-73. PMid:25004470.

Simon C, Shen J, Seip R, Ebbini ES. A robust and computationally efficient algorithm for mean scatterer spacing estimation. IEEE T Ultrason Ferr. 1997; 44(4):882-94.

Tufts DW, Kumaresan R. Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood. Proc IEEE. 1982; 70(9):975-89.

Varghese T, Donohue KD. Characterization of tissue microstructure scatterer distribution with spectral correlation. Ultrason Imaging. 1993; 15(3):238-54. PMid:8879094.

Varghese T, Donohue KD. Mean scatterer spacing estimate with spectral correlation. J Acoust Soc Am. 1994; 96(6):3504-15. PMid:7814765.

Varghese T, Donohue KD. Estimating mean scatterer spacing with the frequency-smoothed spectral autocorrelation function. IEEE T Ultrason Ferr. 1995; 42(3):451-63.

Vautard R, Ghil M. Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D 35. Nonlinear Phenomena. 1989; 35(3):395-424.

Wear KA, Wagner RF, Insana MF, Hall TJ. Application of autoregressive spectral analysis to cepstral estimation of mean scatterer spacing. IEEE Trans Ultrason Ferroelectr Freq Control. 1993; 40(1):50-8. PMid:18263156.

Zhou Z, Wu W, Wu S, Jia K, Tsui PH. A review of ultrasound tissue characterization with mean scatterer spacing. Ultrason Imaging. 2017; 39(5):263. PMid:28797220.

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