# Sidelobes-Free Wavelet-Based Chirp Compression For Ultrasound Imaging

Mohamed Tamraoui, Ralph Abirizk, Ewen Carcreff, Barbara Nicolas, Hervé Liebgott

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To cite this version:

Mohamed Tamraoui, Ralph Abirizk, Ewen Carcreff, Barbara Nicolas, Hervé Liebgott. Sidelobes-Free Wavelet-Based Chirp Compression For Ultrasound Imaging. 2025 IEEE International Ultrasonics Symposium (IUS), Sep 2025, Utrecht, France. pp.1-4, 10.1109/IUS62464.2025.11201375. hal-05379442

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# Sidelobes-Free Wavelet-Based Chirp Compression for Ultrasound Imaging

Mohamed Tamraoui*, Ralph Abirizk†, Ewen Carcreff†, Barbara Nicolas*, Hervé Liebgott*

*Univ Lyon, INSA-Lyon, Universite Lyon 1, CNRS, Inserm, CREATIS UMR 5220, Lyon, France

†The Phased Array Company (TPAC), Nantes, France

mohamed.tamraoui@creatis.insa-lyon.fr

**Abstract**—Chirp-coded excitation improves signal-to-noise ratio in ultrasound imaging, but conventional matched filtering introduces high sidelobes that degrade image quality. Alternatives such as mismatched filtering reduce resolution, while Wiener filtering depends on accurate SNR estimation and may amplify noise. In this work, we adapt the Fourier-Wavelet Regularized Deconvolution (ForWaRD) algorithm for chirp compression, exploiting shrinkage in both Fourier and wavelet domains. Simulations and experiments demonstrate that the proposed wavelet-based filter outperforms conventional methods by combining high axial resolution with strong sidelobe suppression and effective noise reduction.

**Index Terms**—Ultrasound Imaging, Coded excitation, Chirp, Pulse Compression.

## I. INTRODUCTION

Ultrasound imaging is one of the most widely used medical imaging modalities due to its real-time capabilities, portability, and safety, as it does not rely on ionizing radiation. Despite these advantages, ultrasound image quality remains limited, particularly in terms of signal-to-noise ratio (SNR) and contrast. At higher operating frequencies, acoustic waves experience stronger attenuation, which restricts penetration depth and further degrades image quality [1]. While attenuation can be reduced by lowering the transmit frequency, this comes at the expense of spatial resolution. Another approach is to increase the transmitted acoustic energy; however, safety constraints limit the maximum allowable peak pressure [2].

Coded excitation has emerged as a powerful strategy to address these limitations [3], [4]. By transmitting long, modulated sequences and applying pulse compression at reception, coded signals allow more energy to be delivered into tissue without increasing the peak pressure, thereby improving SNR while complying with safety regulations. Among the various coding schemes, chirp-based coded excitation is one of the most widely adopted in ultrasound imaging, as it simultaneously enhances penetration depth and SNR [1], [5].

After transmission, chirp echoes are usually compressed using a matched filter to recover axial resolution [1]. However, matched filtering introduces significant sidelobes—reaching up to 13 dB—that can mask weak scatterers and degrade image contrast. To alleviate this, mismatched filters have been proposed, though at the expense of broadening the mainlobe

This work was supported by the ANR-19-LCV2-0004-01 LabCom Image4US operated by the French National Research Agency (ANR). This work was supported by the LABEX CELYA (ANR-10- LABX-0060), the LABEX PRIMES (ANR-11-LABX-0063) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). This material is based upon work done on the PILoT facility (PILoT, INSA-Lyon).

and reducing axial resolution [2], [5]. Wiener filtering has also been explored, but its performance strongly depends on accurate SNR estimation and can lead to undesirable noise amplification [6].

In this work, we investigate the use of the Fourier-Wavelet Regularized Deconvolution (ForWaRD) algorithm proposed by Baraniuk and co, [7] for chirp signal compression in ultrasound imaging. ForWaRD combines shrinkage operations in both Fourier and wavelet domains, offering a promising compromise between sidelobe suppression and resolution preservation. We demonstrate its potential as a robust alternative to conventional matched, mismatched, and Wiener filtering approaches.

## II. METHODS

### A. General Framework

After transmitting a chirp, the received radio-frequency (RF) signals must be compressed to restore the axial resolution of the echo signal while maximizing the SNR. In this work, we propose a wavelet-based decoding approach derived from the ForWaRD algorithm. The method enhances SNR while preserving both low sidelobes and image resolution.

After transmitting a chirp signal $e(t)$ with the transducer, the received RF signal $y(t)$ can be expressed as

$$y(t) = (e \otimes s)(t) + n(t), \quad (1)$$

where $s(t)$ is the unknown scattered signal and $n(t)$ denotes zero-mean additive white Gaussian noise.

Let $E(f)$ and $Y(f)$ denote the Fourier transforms of the transmitted chirp signal and the received RF data, respectively. The proposed decoding procedure consists of three main steps:

1) **Operator inversion:** The received signal is first inverted in the frequency domain by dividing $Y(f)$ by $E(f)$:

$$\tilde{S}(f) = \frac{Y(f)}{E(f)} = \begin{cases} S(f) + \frac{N(f)}{E(f)}, & |E(f)| > 0, \\ 0, & \text{otherwise,} \end{cases} \quad (2)$$

where $S(f)$ represents the true echo spectrum and $N(f)$ is additive noise. While this operation restores the echo structure, it also amplifies noise in frequency regions where $|E(f)|$ is small.

2) **Fourier shrinkage:** To mitigate noise amplification, Fourier shrinkage is applied using a Wiener-like function:

$$\tilde{S}^{(F)}(f) = \eta_{F}(f) \cdot \tilde{S}(f), \quad \eta_{F}(f) = \frac{|E(f)|^2}{|E(f)|^2 + \gamma}, \quad (3)$$
<figure><img src="image_3.png" /><figcaption>Fig. 1. General pipeline of the proposed wavelet-based compression filter. The Pioneer system transmits a chirp signal, and the received echoes are processed through a three-step wavelet-based compression filter to generate a high-resolution, low-sidelobe compressed signal.</figcaption></figure>

where $\gamma$ is a regularization parameter controlling the amount of Fourier shrinkage. The Fourier representation of the Fourier shrinkage estimate is given by :

$$ 
\begin{aligned}
\tilde{S}^{(F)}(f) &= \tilde{S}(f) \eta_F(f) \\
&= S(f) \left( \frac{|E(f)|^2}{|E(f)|^2 + \gamma} \right) \\
&\quad + \frac{\mathcal{N}(f)}{E(f)} \left( \frac{|E(f)|^2}{|E(f)|^2 + \gamma} \right) \\
&= S^{(F)}(f) + \frac{\mathcal{N}^{(F)}(f)}{E(f)}.
\end{aligned}
\quad (4) $$

Here, $S^{(F)}(f)$ and $\frac{\mathcal{N}^{(F)}(f)}{E(f)}$ denote respectively the retained signal and the leaked noise components. In practice, the operator inversion in (1) and the shrinkage in (4) are typically performed simultaneously to avoid numerical instabilities [7]. The signal is then transformed back to the time domain:

$$ \tilde{s}^{(F)}(t) = \mathcal{F}^{-1}\{\tilde{S}^{(F)}(f)\}. \quad (5) $$

3) **Wavelet shrinkage:** The Fourier-regularized signal is further processed in the wavelet domain:

$$ w_{\ell} = \mathcal{W}\{\tilde{s}^{(F)}(t)\}, \quad (6) $$

where $\mathcal{W}\{\cdot\}$ denotes the wavelet transform. In the wavelet domain, the noise that the Fourier shrinkage step fails to attenuate has significantly reduced energy across all wavelet coefficients, whereas the signal components are strongly represented throughout the wavelet domain. A third step of wavelet shrinkage is then applied using a Wiener-like shrinkage on each wavelet coefficient $w_\ell$:

$$ \hat{w}_{\ell} = \frac{|w_{\ell}|^2}{|w_{\ell}|^2 + \sigma^2} w_{\ell}, \quad (7) $$

where $\sigma^2$ is the estimated noise variance. Finally, the denoised coefficients are inverted back to the time domain:

$$ y_w(t) = \mathcal{W}^{-1}\{\hat{w}_{\ell}\}, \quad (8) $$

yielding the compressed RF signal $y_w(t)$ with enhanced SNR and reduced sidelobes.

## B. Simulation and Experimental Setups

The proposed wavelet-based compression filter was compared against the conventional matched filter, a mismatched filter, and the Wiener compression filter under both simulation and experimental setups.

1) **Simulation Setup:** A 5 MHz linear array transducer with 128 elements was simulated using Field II [8]. The transmitted waveform was a linear chirp of 4 µs duration with a frequency sweep of 4.8 MHz. To evaluate compression performance on RF data, a point spread function (PSF) located at 25 mm depth was first simulated. In addition, a numerical tissue-mimicking phantom was simulated using Synthetic Transmit Aperture (STA) with additive white Gaussian noise band-pass filtered to the transducer bandwidth.

2) **Experimental Setup:** The experimental evaluation was conducted with the 128-channel Pioneer platform from TPAC (West Chester, Ohio, USA). The Philips 5 MHz ATL L7-4 linear array transducer (128 elements, pitch 0.3 mm) was used for plane-wave imaging with four tilted angles (−3°, −1°, 1°, 3°). Measurements were conducted on a wire phantom in water to mimic a PSF and tissue-mimicking phantom containing an anechoic inclusion to assess image contrast. Contrast was quantified using the contrast ratio (CR):

$$ \text{CR [dB]} = 20 \log_{10} \left( \frac{\mu_{\text{cyst}}}{\mu_{\text{bck}}} \right), \quad (9) $$

where $\mu_{\text{cyst}}$ and $\mu_{\text{bck}}$ denote the mean image intensities inside the anechoic inclusion and in the surrounding background, respectively.

# III. RESULTS AND DISCUSSION

## A. Simulation Results

Fig. 2 shows a comparison of the compressed RF signals reflected from a PSF located at 25 mm depth. Noise was added to the RF data to obtain an SNR of 40 dB. The signals
<figure><img src="image_4.png" /><figcaption>Fig. 2. Comparison of simulated pulse-compressed RF signals reflected from a point scatterer at 25 mm using the four compression filters.</figcaption></figure>

were then compressed using the four filters, normalized, and log-compressed. The results highlight the performance of the proposed wavelet-based compression filter in terms of both axial resolution and sidelobe/noise suppression. The matched filter provides good resolution, but exhibits high sidelobe levels, reaching up to -18 dB. The mismatched filter reduces sidelobes to about -27 dB, but at the expense of a wider mainlobe. The Wiener filter preserves axial resolution and even achieves slightly better resolution than the matched filter, but amplifies the noise floor to about -32 dB. In contrast, the proposed wavelet-based filter achieves high resolution comparable to the Wiener filter, while simultaneously suppressing sidelobes and noise.

The B-mode image quality was assessed in simulation using a tissue-mimicking phantom under an SNR of 20 dB with a STA sequence. Fig. 3 shows the reconstructed B-mode images after compression with the four filters. Visual inspection reveals that the anechoic inclusion in the matched filter image contains artifacts originating from compression sidelobes, particularly along the inclusion contour. The mismatched filter image appears more distorted due to severe axial resolution loss, while the Wiener filter image suffers from amplified noise, which obscures the inclusion. In comparison, the proposed wavelet-based filter produces a clear inclusion with reduced artifacts and superior overall image quality.

These qualitative observations are confirmed by quantitative image quality metrics. The -6 dB axial resolution was evaluated on a high-reflecting scatterers, while the CR was measured on the upper anechoic inclusion. In terms of resolution, the mismatched filter performed worst, with a value of 0.44 mm. The matched and Wiener filters achieved resolutions of 0.25 mm and 0.22 mm, respectively. The proposed wavelet-based filter provided the best resolution, with 0.19 mm.

In terms of contrast, the Wiener filter showed the lowest CR due to amplified noise. The matched and mismatched filters

<figure><img src="image_5.png" /><figcaption>Fig. 3. Reconstructed B-mode images obtained after pulse compression of simulated RF data using the four compression filters. Images are displayed with a dynamic range of -60dB.</figcaption></figure>

yielded similar CR values of -26.76 dB and -27.81 dB, respectively. The wavelet-based filter outperformed all methods, with an improved CR value of -29.86 dB.

## B. Experimental Results

Fig. 5 shows a comparison of the compressed RF signals acquired using the Pioneer system and reflected from a wire located at approximately 24 mm depth. The signals were compressed using the four filters, normalized, and log-compressed. Similar to the simulation results, the experimental results highlight the performance of the proposed wavelet-based compression filter compared to the other methods. While the matched, mismatched, and Wiener filters performed similarly, the mismatched filter exhibited a slight disadvantage in terms of mainlobe widening. In contrast, the wavelet-based filter offered a clear advantage by reducing both the noise level and the axial compression sidelobes.

The B-mode image quality was further assessed experimentally using a commercial tissue-mimicking phantom and a plane-wave imaging sequence with four tilted plane waves. Fig. 4 shows the reconstructed B-mode images after pulse compression with the four filters. Visual inspection reveals that the proposed wavelet-based filter produces the highest-quality image, with a clearly visible anechoic inclusion and a strong reduction of artifacts. In comparison, the matched, mismatched, and Wiener filters yield lower-quality images in which the inclusion is partially filled with artifacts originating from compression sidelobes.

These qualitative observations are supported by the measured CR values. The proposed wavelet-based filter achieved a CR of -44.17 dB, significantly outperforming the matched filter (-22.20 dB), mismatched filter (-21.95 dB), and Wiener
<figure><img src="image_6.png" /><figcaption>Fig. 4. Comparison of reconstructed experimental B-mode images of a commercial tissue-mimicking phantom after pulse compression of RF data using the four compression filters. Images are displayed with a dynamic range of -50 dB.</figcaption></figure>

filter (–22.11 dB).

Taken together with the simulation results, these experimen-
tal findings confirm the superiority of the proposed wavelet-
based compression filter for chirp pulse compression. It pro-
vides compressed RF signals with improved axial resolution
and sidelobe suppression, which translates into B-mode images
with better contrast and resolution.

<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison of experimental pulse-compressed RF signals reflected from a wire positioned at approximately 24 mm, obtained using the four compression filters.</figcaption></figure>

IV. CONCLUSION

We proposed a wavelet-based compression filter by ex-
tending the ForWaRD algorithm to chirp-coded ultrasound
imaging. The proposed method combines Fourier and wavelet
shrinkage to achieve pulse compression with high resolution

and reduced sidelobes. Simulations and experiments showed
clear improvements of B-mode image quality over matched,
mismatched, and Wiener filters, with the proposed method
yielding superior axial resolution, noise suppression, and an
experimental contrast ratio of –44 dB compared to –22 dB
for conventional approaches. The method thus offers a robust
solution for chirp compression, with future work aimed at ex-
tending its use to in-vivo imaging and blood flow applications.

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