# Dual-/tri-apodization techniques for high frequency ultrasound imaging: a simulation study

- Jin Ho Sung
^{1}and - Jong Seob Jeong
^{1}Email author

**13**:143

https://doi.org/10.1186/1475-925X-13-143

© Sung and Jeong; licensee BioMed Central Ltd. 2014

**Received: **29 August 2014

**Accepted: **5 October 2014

**Published: **11 October 2014

## Abstract

### Background

In the ultrasound B-mode (Brightness-mode) imaging, high side-lobe level reduces contrast to noise ratio (CNR). A linear apodization scheme by using the window function can suppress the side-lobe level while the main-lobe width is increased resulting in degraded lateral resolution. In order to reduce the side-lobe level without sacrificing the main-lobe width, a non-linear apodization method has been suggested.

### Methods

In this paper, we computationally evaluated the performance of the non-linear apodization method such as dual-/tri-apodization focusing on the high frequency ultrasound image. The rectangular, Dolph-Chebyshev, and Kaiser window functions were employed to implement dual-/tri-apodization algorithms. The point and cyst target simulations were conducted by using a dedicated ultrasound simulation tool called Field-II. The center frequency of the simulated linear array transducer was 40 MHz and the total number of elements was 128. The performance of dual-/tri-apodization was compared with that of the rectangular window function focusing on the side-lobe level and the main-lobe widths (at -6 dB and -35 dB).

### Results

In the point target simulation, the main-lobe widths of the dual-/tri-apodization were very similar to that of the rectangular window, and the side-lobe levels of the dual-/tri-apodization were more suppressed by 9 ~ 10 dB. In the cyst target simulation, CNR values of the dual-/tri-apodization were improved by 41% and 51%, respectively.

### Conclusions

The performance of the non-linear apodization was numerically investigated. In comparison with the rectangular window function, the non-linear apodization method such as dual- and tri-apodization had low side-lobe level without sacrificing the main-lobe width. Thus, it can be a potential way to increase CNR maintaining the main-lobe width in the high frequency ultrasound imaging.

## Background

In the diagnostic ultrasound imaging by using an array transducer, a beamforming technique is commonly used for electrical transmit/receive focusing, beam steering, and dynamic focusing. A conventional delay and sum (DAS) beamforming enhances the signals from the selected location and reduces the signals from undesired direction by compensating arrival time of received signals. Although the conventional DAS beamforming can increase the energy of the ultrasound beam at the focal point, the side-lobe level also increases resulting in degraded contrast to noise ratio (CNR) [1].

In order to reduce the side-lobe level, linear apodization methods by using various window functions were developed. The window functions realized by changing the amplitude of the signals can effectively suppress the side-lobe level. However, the main-lobe width is increased resulting in reduced lateral resolution.

To solve this problem, some researchers have proposed several methods such as constrained least squares (CLS), non-linear apodization, and dual-apodization with cross-correlation (DAX) methods [2–8]. Among them, the non-linear apodization method especially multi-apodization technique can be easily implemented and the processing time is short compared to other methods. However, the performance was mainly demonstrated by impulse response plotting without applying to ultrasound imaging [4].

In this study, we computationally evaluated the performance of dual-/tri-apodization focusing on the high-frequency ultrasound imaging since it suffers from high side-lobe level and noise components. A Field-II, a dedicated ultrasound simulation tool, was employed for this demonstration. The rectangular, Dolph-chebyshev, and Kaiser window functions were chosen for dual-/tri-apodization. The point and cyst target simulations were conducted and subsequently the main-lobe width, the side-lobe level, and CNR value were measured. The simulation results show that dual-/tri-apodization can effectively suppress the side-lobe level and increase CNR without degrading lateral resolution in the high-frequency ultrasound imaging.

## Methods

### A. Selection of window functions

The rectangular, Dolph-Chebyshev, and Kaiser window functions were chosen for dual- and tri-apodization since the rectangular window function has the narrowest main-lobe width, and other window functions can control the main-lobe width and the side-lobe level by adjusting parameters. Before explaining the principle of dual-/tri-apodization, the features of used window functions were discussed.

*n*is the sample number in time domain. The discrete Fourier transform (DFT) of the rectangular window function can be defined by

where *k* is the sample number in frequency domain.

*W*

_{ D-C }

*(k)*is the DFT of the Dolph-Chebyshev window function and it is defined by equation (4) [9–13].

*β*is defined as

where *α* in (5) is the log of the ratio of main-lobe level to side-lobe level and (-1)^{
k
} in (4) expresses the shifted origin in the time domain signal.

*α*

_{ K }which determines the main-lobe width and the side-lobe level. Note that the subscript

*K*is named after the Kaiser window function. The Kaiser window function in time domain is defined as [14]

*α*

_{ K }is a control parameter and

*I*

_{0}(

*X*) is the zero-order modified Bessel function defined as

### B. Principle and effect of dual-/tri-apodization

Since the rectangular window function has the narrowest main-lobe width, and the Dolph-Chebyshev and Kaiser window functions have the control parameter which can be optimized depending on applications, we chose the rectangular, Dolph-Chebyshev, and Kaiser window functions for dual-/tri-apodization. The rectangular and Dolph-Chebyshev window functions were used for dual-apodization. In dual-apodization method, the rectangular and Dolph-Chebyshev window functions were applied to input signal making two different output signals. After that, those output signals were normalized by themselves and minimum value of them was selected. Consequently, the main-lobe width and the side-lobe level of the dual-apodization method were identical to the main-lobe width of the rectangular window function and the side-lobe level of the Dolph-Chebyshev window function, respectively. As a similar way, the rectangular, Dolph-Chebyshev, and Kaiser window functions were used for tri-apodization. Each singular window function was applied to input signal respectively making three different output signals, and the same procedure in the dual-apodization was conducted. As a result, tri-apodization also had narrow main-lobe width identical to that of the rectangular window function, and had low side-lobe level affected by the Dolph-Chebyshev and Kaiser window functions. In this paper, we chose control parameters of the Dolph-Chebyshev (*α*) and Kaiser (*α*
_{
K
}) window functions as 2.5 and 2.5/π, respectively, to optimize the performance of the dual- and tri-apodization.

*α*= 2.5 to decrease near field side-lobe level of dual-apodization by -50 dB and to obtain 1.85 bins main-lobe width at -6 dB.

In the ultrasound image, the side-lobe level should be less than -40 dB because the ultrasound image contrast is determined by the lateral point response at -40 dB
[15]. Furthermore, the near field side-lobe level of dual-apodization can be suppressed by the selection of minimal value procedure. Additionally, that is affected by the first cross point between the rectangular and Dolph-Chebyshev window responses. Therefore, considering -40 dB side-lobe level criterion for contrast, we chose the control parameter of the Dolph-Chebyshev window function, *α*, as 2.5.Figure
1(d) shows IPR of dual-apodization and it had 1.21 bins main-lobe width at -6 dB, which is identical to that of the rectangular window function. The highest side-lobe level of dual-apodization is slightly lower than that of the rectangular window function due to the effect of the main-lobe width of the Dolph-Chebyshev window function. The rest of side-lobe level was -50 dB due to the side-lobe level of the Dolph-Chebyshev window function.

To more suppress the first side-lobe level of dual-apodization, we employed the Kaiser window function and subsequently realized tri-apodization as shown in Figure
1(e). The main-lobe width of the Kaiser window function can exist between the rectangular and Dolph-Chebyshev window functions, and the first side-lobe level can be lower than dual-apodization depending on a control parameter. When we choose *α*
_{
K
} =2.5/π, the highest side-lobe level of the Kaiser window function was -21 dB and -6 dB main-lobe width was 1.43 bins (Figure
1(c)). Those specifications contribute the improved performance of the tri-apodization compared to the rectangular function. The main-lobe width was identical, the first side-lobe level was 7 dB low, and the harmonic side-lobe level was -50 dB.

### C. Specification of B-mode simulation

**Simulated parameters of 128 element linear array transducer**

Parameter | Value |
---|---|

Total Number of Elements | 128 |

Number of Elements in Subaperture | 32 |

Number of Scanlines | 128 |

Center Frequency [MHz] | 40 |

Element Pitch [μm] | 40 |

Speed of Sound [m/s] | 1500 |

Transmit Focus [mm] | 3.5 |

## Simulation results

### A. Point target B-mode simulation

**-6 dB Main-lobe widths of the singular window functions, and dual-/tri-apodization**

Rectangular window [μm] | Dolph-Chebyshev window [μm] | Kaiser window [μm] | Dual-apodization [μm] | Tri-apodization [μm] | |
---|---|---|---|---|---|

1st target | 90.7 | 132.2 | 101.2 | 91.5 | 91.5 |

2nd target | 91.2 | 103.4 | 93.1 | 91.2 | 91.2 |

3rd target | 90.4 | 103.2 | 96.3 | 91.1 | 91.1 |

4th target | 102.8 | 123.3 | 112.0 | 103.8 | 103.8 |

5th target | 124.5 | 163.9 | 141.2 | 126.0 | 126.0 |

**-35 dB Main-lobe widths of the singular window functions and dual-/tri-apodization**

Rectangular window [μm] | Dolph-Chebyshev window [μm] | Kaiser window [μm] | Dual-apodization [μm] | Tri-apodization [μm] | |
---|---|---|---|---|---|

1st target | 486.1 | 351.0 | 367.7 | 351.0 | 331.6 |

2nd target | 386.6 | 350.1 | 298.2 | 350.1 | 298.2 |

3rd target | 386.7 | 375.3 | 261.5 | 370.0 | 239.2 |

4th target | 482.3 | 453.0 | 349.4 | 453.0 | 350.8 |

5th target | 624.9 | 537.3 | 463.1 | 537.3 | 464.2 |

**Side-lobe levels of the singular window functions and dual-/tri-apodization**

Rectangular window [dB] | Dolph-Chebyshev window [dB] | Kaiser window [dB] | Dual-apodization [dB] | Tri-apodization [dB] | |
---|---|---|---|---|---|

1st target | -39 ~ -45 | -46 ~ -52 | -47 ~ -51 | -49 ~ -54 | -52 ~ -55 |

2nd target | -44 ~ -48 | -53 ~ -57 | -49 ~ -54 | -53 ~ -57 | -53 ~ -57 |

3rd target | -43 ~ -48 | -54 ~ -56 | -51 ~ -54 | -54 ~ -57 | -54 ~ -57 |

4th target | -39 ~ -45 | -48 ~ -51 | -47 ~ -50 | -48 ~ -54 | -50 ~ -54 |

5th target | -35 ~ -40 | -40 ~ -48 | -41 ~ -46 | -40 ~ -48 | -42 ~ -49 |

### B. Cyst target B-mode simulation

where *S*
_{
i
} is the mean brightness value of the cyst target inside, *S*
_{
o
} is the mean brightness value of the cyst target outside, *σ*
_{
i
} is the variance of the cyst target inside, and *σ*
_{
o
} is the variance of the cyst target outside.

**CNR values of the singular window functions and dual-/tri-apodization**

Rectangular window | Dolph-Chebyshev window | Kaiser window | Dual-apodization | Tri-apodization | |
---|---|---|---|---|---|

CNR | 2.58 | 4.26 | 3.71 | 3.64 | 3.90 |

## Discussion

In the point target simulation, the beam projection method capable of averaging the main-lobe width and the side-lobe level along the axial direction was employed to obtain more accurate results. The -6 dB main-lobe widths of dual- and tri-apodization were almost same as that of the rectangular window function. The -35 dB main-lobe widths of dual- and tri-apodization were 16.7 μm and 147.5 μm narrower than that of the rectangular window function at the focal point. In the case of point target simulation with a pulsed wave field, the boundary between main-lobe and side-lobe is not clear. Therefore, in order to compare the main-lobe widths of other windows or schemes, we defined -35 dB as a criterion considering -40 dB normal dynamic range in a B-mode image. In this level, some side-lobes of the rectangular window might be included as a main-lobe. Thus, -35 dB main-lobe width of rectangular window was broader than other schemes which have much smaller side-lobe level compared to the rectangular window. The side-lobe levels of dual-/tri-apodization were more suppressed by 9 ~ 10 dB. In the cyst target simulation, the Dolph-Chebyshev window had the highest CNR value and it was followed by tri-apodization, the Kaiser window, dual-apodization and the rectangular window in order. Because the side-lobe level of each window function was -13 dB, -50 dB, and -21 dB in order of the rectangular, Dolph-Chebyshev, and Kaiser window, the Dolph-Chebyshev window had the highest CNR value and the rectangular window had the lowest CNR value. In the case of dual-apodization, the first side-lobe level was similar with that of the rectangular window but the rest side-lobe level was about -50 dB. As a result, CNR value of dual-apodization existed between the rectangular window and Dolph-Chebyshev window. Additionally, since the highest side-lobe level of dual-apodization was higher than that of the Kaiser window, CNR value of the Kaiser window was followed by that of dual-apodization. In the case of tri-apodization, the highest side-lobe level was similar with that of the Kaiser window but the rest side-lobe level was lower than that of the Kaiser window until the Kaiser window has lower side-lobe level than that of the Dolph-Chebyshev window where the Kaiser window has -50 dB side-lobe level at the first time. Therefore, tri-apodization had higher CNR value than that of the Kaiser window. Consequently, CNR values of dual-/tri-apodization were 41% and 51% improved respectively compared with that of the rectangular window. Because dual- and tri-apodization are examples of the multi-apodization technique, the more window functions with lower side-lobe level used, the better CNR value can be obtained. However, this technique selects minimal value of images after applying different window functions, so the main-lobe pattern of added window function should cross the highest side-lobe resulting in suppression of the side-lobe. Thus, the control parameters determining the main-lobe width and the side-lobe level of each window function should be carefully chosen considering aforementioned issues. It has been well known that the first side-lobe level depends on the amplitude weighting function (apodization), and the high side-lobe called the grating lobe is affected by the element pitch size. Increasing the pitch size causes appearance of the grating lobe inside the view width. On the contrary, the lateral resolution affected by f-number (focal length/aperture size) is improved under the fixed number of elements in the subaperture. In this paper, we used the 128 element linear array transducer with 40 μm pitch. The pitch was slightly larger than one wave-length resulting in grating lobe appearance at 70 degree. However, the effects of the grating lobe can be negligible in this study due to the limited view width [18].

## Conclusions

In this study, the performance of the non-linear apodization was numerically investigated by applying to the high frequency ultrasound imaging. We demonstrated that dual- and tri-apodization can successfully suppress the side-lobe level without sacrificing lateral resolution resulting in increased CNR value. Therefore, dual- and tri-apodization can be one of the potential ways to effectively improve spatial and contrast resolution of a high frequency ultrasound B-mode image.

## Declarations

### Acknowledgements

This research was supported by R&D Program of ministry of Trade, industry and Energy/Korea Evaluation institute of industrial Technology (Grant No, MOTIE/KEIT 10048528, Development of ICT based Wireless Ultrasound Solution for Point-of-Care Applications), International Collaborative R&D Program (N01150049) funded by the Ministry of Trade, Industry & Energy (MOTIE), Korea (N01150049, Developing high frequency bandwidth [40 ~ 60 MHz] high resolution image system and probe technology for diagnosing cardiovascular lesion), and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1044159).

## Authors’ Affiliations

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