Improved Attenuation Estimation of Ultrasonic Signals Using Frequency Compounding Method

  • Kim, Hyungsuk (Department of Electrical Engineering, Kwangwoon University) ;
  • Shim, Jaeyoon (Department of Electrical Engineering, Kwangwoon University) ;
  • Heo, Seo Weon (School of Electronic and Electrical Engineering, Hongik University)
  • Received : 2016.11.26
  • Accepted : 2017.07.27
  • Published : 2018.01.01


Ultrasonic attenuation is an important parameter in Quantitative Ultrasound and many algorithms have been proposed to improve estimation accuracy and repeatability for multiple independent estimates. In this work, we propose an improved algorithm for estimating ultrasonic attenuation utilizing the optimal frequency compounding technique based on stochastic noise model. We formulate mathematical compounding equations in the AWGN channel model and solve optimization problems to maximize the signal-to-noise ratio for multiple frequency components. Individual estimates are calculated by the reference phantom method which provides very stable results in uniformly attenuating regions. We also propose the guideline to select frequency ranges of reflected RF signals. Simulation results using numerical phantoms show that the proposed optimal frequency compounding method provides improved accuracy while minimizing estimation bias. The estimation variance is reduced by only 16% for the un-compounding case, whereas it is reduced by 68% for the uniformly compounding case. The frequency range corresponding to the half-power for reflected signals also provides robust and efficient estimation performance.

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Fig. 1. Illustrative weighting factors of the combiningmethods. Seven frequency components are selectedcentered at 5MHz, with a frequency step of 0.5MHz. The dashed line is assumed to be a powerspectrum of the received signals: (a) Uniformweight combining, and (b) Optimal weightcombining

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Fig. 2. Estimated attenuation coefficients over the entiredepth. The attenuation coefficients for the referencephantom and sample are 0.3 and 0.5 dB/cm/MHz,respectively, and the beam focus is set to 40 mm.The errorbars represent the estimation variances ateach depth

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Fig. 3. Estimation variances for the number of frequencycomponents. The frequency components areselected centered at the centroid of power spectrumat each depth with a frequency step of 0.1MHz: (a)20mm, and (b) 40mm

Table 1. Simulation parameters of a numerical phantom

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Supported by : National Research Foundation of Korea(NRF), Kwangwoon University


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