# Complementary Coded Multiplane Wave Sequence for SNR Increase in 3D Ultrafast Power Doppler Ultrasound Imaging

Mohamed Tamraoui, Emmanuel Roux, Hervé Liebgott

► To cite this version:

Mohamed Tamraoui, Emmanuel Roux, Hervé Liebgott. Complementary Coded Multiplane Wave Sequence for SNR Increase in 3D Ultrafast Power Doppler Ultrasound Imaging. 2024 IEEE Ultrasonics, Ferroelectrics, and Frequency Control Joint Symposium (UFFC-JS), Sep 2024, Taipei, Taiwan. pp.1-4, 10.1109/UFFC-JS60046.2024.10793876. hal-04947776

HAL Id: hal-04947776

https://hal.science/hal-04947776v1

Submitted on 14 Feb 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Complementary Coded Multiplane Wave Sequence for SNR Increase in 3D Ultrafast Power Doppler Ultrasound Imaging

Mohamed Tamraoui

Emmanuel Roux

Hervé Liebgott

Univ Lyon, INSA-Lyon, Université Lyon
CNRS, Inserm, CREATIS UMR 522

Univ Lyon, INSA-Lyon, Université Lyon
CNRS, Inserm, CREATIS UMR 522

Univ Lyon, INSA-Lyon, Université Lyon
CNRS, Inserm, CREATIS UMR 522

Lyon, France

Lyon, France

Lyon, France

mohamed.tamraoui@creatis.insa-lyon.fr

emmanuel.roux@creatis.insa-lyon.fr

herve.liebgott@creatis.insa-lyon.fr

**Abstract**—Ultrafast 3D Power Doppler ultrasound imaging, enhances blood flow detection and offers detailed volumetric assessments of blood flow. However, techniques like CPWC face SNR limitations, especially at high frame rates. This study introduces a novel method using 2D sparse arrays and Multi-Plane Wave Imaging with Complete Complementary Codes (MPWI-3C), which improves SNR without increasing the number of transmissions. Experimental results demonstrate that MPWI-3C outperforms existing methods, offering superior sensitivity and image quality, particularly in challenging deep tissue imaging scenarios.

**Index Terms**—3D Power Doppler, Sparse Arrays, Coded Excitation

## I. INTRODUCTION

Power Doppler ultrasound is a sophisticated imaging technique that enhances blood flow assessment by measuring the amplitude of Doppler signals rather than velocity, making it more sensitive to weak blood flow compared to color Doppler ultrasound [1]. Integrating three-dimensional (3D) ultrasound imaging with power Doppler provides comprehensive volumetric assessments, capturing vascular details often missed by two-dimensional (2D) imaging, which is confined to a single plane. Ultrafast Doppler imaging using coherent plane wave compounding (CPWC) has significantly boosted power Doppler sensitivity, increasing it up to 30 times compared to conventional focused imaging due to high temporal correlation between frames [2]. However, CPWC faces a trade-off: increasing the number of angles improves image quality but lowers the frame rate, and fewer plane waves, while preserving frame rates, reduce signal-to-noise ratio (SNR), particularly in patients with thick tissue or bone that attenuate acoustic waves.

Additionally, 3D ultrasound imaging can be effectively performed using sparse arrays [3], addressing the challenges posed by the high element count in 2D matrix arrays, which often limits their use in high frame rate applications. Sparse arrays offer the advantage of having each probe element continuously connected to beamforming channels during both transmission and reception, eliminating the need for multiple transmissions to capture the RF data for the entire array, as

required in multiplexed matrix arrays. However, sparse arrays are typically designed with small transducer elements that have high impedance and a reduced active area. This combination of high impedance and small active area contributes to low sensitivity, resulting in a reduced SNR, which can affect image quality.

Coded excitation is an effective technique for increasing the SNR in ultrasound imaging by increasing transmitted energy without compromising axial resolution or violating safety limits. Introduced in [4], Multiplane Wave Imaging method with Hadamard encoding (MPWI-HD) improves the SNR of CPWC by quasi-simultaneously transmitting multiple tilted plane waves, each encoded with Hadamard coefficients. The received signals are decoded through basic addition/subtraction operations to separate each plane wave's contribution, boosting the SNR by 10 log10(N) compared to conventional CPWC, where N is the number of plane waves. MPWI-HD has shown improved Doppler sensitivity in ultrafast imaging of the rat brain through the skull, allowing for the detection of deeper blood vessels. However, SNR improvement still depends on the number of transmitted plane waves, and if this number is limited by technology, further SNR enhancement is not possible.

In this context, our study presents a novel method to enhance the SNR in 3D power Doppler imaging by using sparse arrays. This technique aims to improve SNR without increasing the number of transmissions. It builds on the MPWI method but replaces the Hadamard matrix with Complete Complementary Codes (CCC) [5]. These codes, denoted as (M, N, L)-CCC, consist of M sets of N binary sequences each with L bits. They are renowned for their ideal autocorrelation (delta impulse) and ideal cross-correlation (zero at all shifts), making them well-suited for simultaneous sequence transmission.

## II. METHODS

### A. MPWI-3C

MPWI-HD enhances the SNR of recovered RF signals, but its effectiveness is limited by the number of transmitted plane waves. To overcome this limitation, in MPWI-3C, *N* plane waves are transmitted quasi-simultaneously during each transmission event. Each plane wave is assigned a set of (*N*, *N*, *MN*/*P*)-CCC sequences, with *L*=*MN*/*P* is the length

<footnote>This work was supported by the LABEX PRIMES under Grant ANR-11-LABX-0063 of Université de Lyon, through the Program "In-´ vestissements d'Avenir" under Grant ANR-11-IDEX-0007 operated by the French National Research Agency (ANR), performed within the framework of the ANR-20-CE19-0023 SPARTECHUS. This material is based upon work done on the PILOT facility (PILOT, INSA-Lyon).</footnote>
Step I: Transmission

<figure><img src="image_2.png" /><figcaption>Fig. 1: MPWI-3C imaging transmission and decoding scheme using (N, N, MN/P)-CCC.</figcaption></figure>

of each binary sequence. For more details on the generation process of CCC refer to [5]. Each tilted plane wave will be transmitting a different binary sequence from its assigned set. Due to the high harmonic content of binary (N, N, MN/P)-CCC sequences, they are not transmitted directly. Instead, these sequences modulate a base pulse e(t), a sine wave at the transducer's central frequency, to optimize the use of the transducer's bandwidth.

After each of the N transmissions, the RF signals are decoded using the ideal autocorrelation and cross-correlation properties of CCC to isolate the contribution of each plane wave without interference. Consequently, the ultrafast plane wave data set is retrieved as if a single plane wave had been transmitted during each event, but with a significantly higher SNR. The SNR gain with this method is $10 \log_{10}(NL)$, where $L = MN/P$ represents the number of bits in the sequences, which surpasses the $10 \log_{10}(N)$ SNR gain achieved by MPWI-HD. Furthermore, in MPWI-3C, the SNR enhancement is dependent not only on the number of transmissions N but also on the length of the binary sequences. This allows for increased SNR by extending the length of the sequences while maintaining a fixed number of transmissions, in contrast to MPWI-HD, where additional transmissions are necessary for further SNR improvement.

To illustrate the principal of MPWI-3C, we detail the example of two transmissions ($N=2$) with two tilted plane waves $\alpha_1$ and $\alpha_2$ and the corresponding decoding process in Fig. 1:

$$C = \begin{bmatrix} s_{1,1} & s_{1,2} \\ s_{2,1} & s_{2,2} \end{bmatrix} \quad (1)$$

Sequences $s_{1,1}$ and $s_{1,2}$ are assigned for the plane wave angled at $\alpha_1$, while sequences $s_{2,1}$ and $s_{2,2}$ are assigned to the

plane wave angled at $\alpha_2$. During the first transmission, these plane waves are emitted quasi simultaneously with a minimal time delay $\tau$ to prevent overlap. Specifically, the plane wave at $\alpha_1$ sends sequence $s_{1,1}$ modulated by the base pulse e(t), and the plane wave at $\alpha_2$ transmits sequence $s_{2,1}$ similarly modulated. In the subsequent transmission, the plane waves emit sequences $s_{1,2}$ and $s_{2,2}$, respectively.

The decoding process exploits the ideal autocorrelation and cross-correlation characteristics of CCC to separate the contributions of each plane wave. After the initial transmission, the received signals are correlated with sequences $s_{1,1}$ and $s_{2,1}$. After the second transmission, signals are correlated with $s_{1,2}$ and $s_{2,2}$. Due to the ideal correlation properties, this decoding isolates the signal from the $\alpha_1$ and $\alpha_2$ plane waves, enhancing their amplitude. The amplitude gain is of $2L$. With parameters $M=2$ and $P=1$, a 4-bit sequence can be generated, providing an SNR gain of $10 \log_{10}(N.L) = 10 \log_{10}(8) = 9$ dB, surpassing the gain achieved with MPWI-HD ($10 \log_{10}(N) = 10 \log_{10}(2) = 3$ dB).

## B. Experimental setup

The proposed MPWI-3C was experimentally compared with CPWC and MPWI-HD using the Vantage-256 research scanner (Verasonics, Inc., Kirkland, WA, USA). A 2D sparse array with 256 elements, optimized based on the Vermon 2-D matrix array (Vermon S.A., Tours, France), was used. The array features a central frequency of 7.2 MHz, a 300 µm pitch, and element dimensions of 300 × 300 µm. Sparse array optimization was performed using simulated annealing, considering the matrix array's multiplexing constraints. Four plane waves, tilted at $\pm 2^\circ$ in both directions, were transmitted at a frame rate of 800 Hz. For the MPWI-3C method, a (4, 4, 4)-CCC code was utilized. All methods used the Arbitrary
Waveform Generation Toolbox (ArbWave) provided by the Vantage scanner to convert binary sequences into tristate signals suitable for transmission.

<figure><img src="image_3.png" /><figcaption>Fig. 2: Experimental power Doppler setup. (a) optimized 2D sparse array (b) custom build flow phantom.</figcaption></figure>

Flow experiments were conducted using a custom-built flow phantom consisting of two 4 mm tubes: one positioned in the probe's near field, where SNR is high, and the other in a deeper region with low SNR due to attenuation. A Doppler fluid with a flow velocity of 23 cm/s was pumped through the tubes using a commercial flow pump (Model 769, CIRS). The performance of CPWC, MPWI-HD, and MPWI-3C in power Doppler imaging was compared in terms of SNR and contrast ratio (CR) using standard evaluation metrics :

$$SNR_{dB} = 20 * \log_{10} \left( \frac{\sqrt{\sum_{n=1}^{N_p} |I_s(n)|^2}}{\sqrt{\sum_{n=1}^{N_p} |I_n(n)|^2}} \right) \quad (2)$$

$$CR_{dB} = 20 * \log_{10} \left( \frac{\mu_s}{\mu_n} \right) \quad (3)$$

The SNR was used to evaluate the strength of the blood flow signal, calculated as the ratio of the blood flow signal power to the noise power. Specifically, $I_s$ and $I_n$ denote the intensities of pixels within the blood flow region and the noise region (outside the flow), respectively, with the same number of pixels $N_p$. To assess blood flow detectability, the CR was calculated on power Doppler images, using the mean intensities $\mu_{cyst}$ and $\mu_{bck}$, corresponding to regions inside and outside the blood flow area, respectively.

### III. RESULTS

In this section, we evaluate and compare the performance of the three imaging methods—CPWC, MPWI-HD, and the proposed MPWI-3C—in 3D power Doppler imaging. To create the power Doppler maps, 200 ultrafast frames were captured at a frame rate of 800 Hz and then processed using the Delay-And-Sum (DAS) beamformer. The beamformed images were filtered to remove static tissue signals using a singular value decomposition (SVD) filter, retaining only blood flow and

noise. The resulting data were then summed to generate the power Doppler images. Notably, the noise was not filtered with SVD to better demonstrate the impact of MPWI-HD and MPWI-3C on the noise levels.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Experimental power Doppler maps of the closer tube using CPWC, MPWI-HD, and MPWI-3C methods with four plane wave transmissions.</figcaption></figure>

#### A. Closer tube: High SNR region

Fig. 3 shows experimental xz and yz slices from the 3D power Doppler maps of the tube positioned near the probe at approximately 18 mm for each of the imaging methods (CPWC, MPWI-HD, and MPWI-3C) using four plane wave transmissions. Given that the tube is located in a high SNR region, all methods produce high-quality power Doppler maps with visible flow signals, though with varying strengths. The results indicate that CPWC generates the power Doppler map with the weakest flow signal due to its inherently lower transmission SNR. Both MPWI-HD and MPWI-3C produce stronger power Doppler maps, with MPWI-3C showing a slight edge in signal strength. These visual assessments are corroborated by calculating the image quality metrics and the results are represented in TABLE I. MPWI-HD and MPWI-3C have similar SNR and CR values with advantage to the proposed methods of almost 1.65dB for both methods.

#### B. Deeper tube: Low SNR region

Fig. 4 presents xz and yz slices from the 3D power Doppler maps of the tube positioned in a deep region (approximately 60 mm) for the imaging methods: CPWC, MPWI-HD, and the proposed MPWI-3C, each utilizing four plane wave transmissions. Due to the low SNR environment, the CPWC method generates a power Doppler map of very poor quality.
with a high noise level that makes it difficult to distinguish the flow within the tube from surrounding tissue. MPWI-HD improves flow visibility but is still insufficient for clear differentiation from the surrounding noise, resulting in a power Doppler map with a high noise level that affects overall image quality. In contrast, MPWI-3C achieves the highest quality power Doppler map, effectively suppressing noise and clearly highlighting the flow signal. These observations are validated by quantitative image quality metrics presented in TABLE I, where MPWI-3C shows superior performance with the highest SNR (-36.78 dB) and CR (-31.90 dB) compared to CPWC and MPWI-HD.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Experimental power Doppler maps of the deeper tube using CPWC, MPWI-HD, and MPWI-3C methods with four plane wave transmissions.</figcaption></figure>

<table><caption>TABLE I: SNR and CR comparison between the three imaging methods</caption><thead><tr><th>Region</th><th>Imaging Method</th><th>SNR (dB)</th><th>CR (dB)</th></tr></thead><tbody><tr><td rowspan="3">Closer Tube</td><td>CPWC</td><td>40.36</td><td>-34.66</td></tr><tr><td>MPWI-HD</td><td>47.01</td><td>-41.89</td></tr><tr><td>MPWI-3C</td><td>48.67</td><td>-43.56</td></tr><tr><td rowspan="3">Deeper Tube</td><td>CPWC</td><td>12.27</td><td>-7.37</td></tr><tr><td>MPWI-HD</td><td>23.45</td><td>-18.34</td></tr><tr><td>MPWI-3C</td><td>36.78</td><td>-31.90</td></tr></tbody></table>

IV. DISCUSSION

In this study, we proposed a novel coded excitation method, MPWI-3C, to enhance the SNR of 3D power Doppler imaging using 2D sparse arrays. The MPWI-3C approach uses Complete Complementary Codes (CCC) to increase SNR without necessitating additional transmissions, instead simply extending the length of binary sequences. This characteristic

effectively addresses a critical limitation in CPWC and MPWI-HD, where SNR enhancement is restricted by the number of transmitted plane waves.

Experimental results demonstrate the efficacy of MPWI-3C in both high and low SNR conditions. In close regions imaging scenarios, where SNR is naturally higher, both MPWI-3C and MPWI-HD outperformed CPWC, showing similar performance. Specifically, MPWI-3C achieved SNR gains of 8.31 dB and 1.65 dB compared to CPWC and MPWI-HD, respectively. The distinct advantage of MPWI-3C became evident in deeper imaging scenarios, where the SNR is extremely low. The noise was substantially reduced, allowing clearer differentiation of blood flow signals from surrounding tissues using the proposed MPWI-3C. In these challenging conditions, MPWI-3C produced SNR gains of 24.51 dB and 13.32 dB over CPWC and MPWI-HD, respectively.

While increasing the number of transmissions can enhance SNR, it may also lead to an expansion of the blind zone area, particularly when longer sequences are used. This potential limitation will be explored in future works by considering simultaneous plane wave transmissions or employing different probes for transmission and reception. Another limitation to be addressed is the effect of motion on the decoding process. Since CCC relies on complementarity properties, severe motion in the imaging medium can generate sidelobes during decoding, which degrades image contrast.

Overall, MPWI-3C offers a robust solution for enhancing SNR in 3D power Doppler imaging, especially in challenging deep tissue environments using sparse arrays. Future work will explore other applications such as color Doppler imaging and elastography to further validate the versatility and efficacy of the MPWI-3C approach.

REFERENCES

[1] J. M. Rubin, R. S. Adler, J. B. Fowlkes, S. Spratt, J. E. Pallister, J.-F. Chen, and P. L. Carson, "Fractional moving blood volume: estimation with power doppler us." *Radiology*, vol. 197, no. 1, pp. 183-190, 1995.

[2] E. Mace, G. Montaldo, B.-F. Osmanski, I. Cohen, M. Fink, and M. Tanter, "Functional ultrasound imaging of the brain: theory and basic principles," *IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control*, vol. 60, no. 3, pp. 492-506, Mar. 2013. [Online]. Available: http://ieeexplore.ieee.org/document/6470411/

[3] E. Roux, A. Ramalli, H. Liebgott, C. Cachard, M. C. Robini, and P. Tortoli, "Wideband 2-D Array Design Optimization With Fabrication Constraints for 3-D US Imaging," *IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control*, vol. 64, no. 1, pp. 108-125, Jan. 2017. [Online]. Available: https://ieeexplore.ieee.org/document/7581110/

[4] E. Tiran, T. Deffieux, M. Correia, D. Maresca, B.-F. Osmanski, L.-A. Sieu, A. Bergel, I. Cohen, M. Pernot, and M. Tanter, "Multiplane wave imaging increases signal-to-noise ratio in ultrafast ultrasound imaging," *Physics in Medicine and Biology*, vol. 60, no. 21, pp. 8549-8566, Nov. 2015. [Online]. Available: https://iopscience.iop.org/article/10.1088/0031-9155/60/21/8549

[5] M. Tamraoui, H. Liebgott, and E. Roux, "Complete Complementary Coded Excitation Scheme for SNR Improvement of 2D Sparse Array Ultrasound Imaging," *IEEE Transactions on Biomedical Engineering*, pp. 1-14, 2023. [Online]. Available: https://ieeexplore.ieee.org/document/10287569/