Lee, Chung, Yoon, and Song: Adaptive singular value decomposition filtering of high-intensity focused ultrasound interference enables real-time ultrasound-guided therapy


High-intensity focused ultrasound (HIFU) is an emerging therapeutic tool for the effective thermal ablation of pathological tissue. For accurate localization of the target and safe control of the HIFU dosage, real-time imaging guidance during the HIFU exposure is desired. Ultrasound imaging has the capability to guide clinicians toward a lesion in real time, but is not an ideal option, as HIFU application causes strong interference, thereby substantially distorting the images used for guidance. Thus, this study introduces singular value decomposition–based filtering capable of restoring ultrasound harmonic images from HIFU interference without undesirable spectral distortion. The results were experimentally validated with a custom-made phantom, indicating that this approach effectively eliminates HIFU-induced artifacts, which is essential for real-time monitoring of the therapeutic process.

Key points

Real-time imaging during high-intensity focused ultrasound (HIFU) exposure is critical for accurate, reliable treatment. Adaptive singular value decomposition filtering can remove the HIFU interferences effectively.


High-intensity focused ultrasound (HIFU) selectively and remotely ablates abnormal tissue, including malignant cancer, in the body with focused acoustic energy [1,2]. Compared to classical open surgery and radioactivity-based therapeutic approaches, HIFU can offer faster recovery times, less pain, limited tissue damage, and fewer infections [3]. For example, the HIFU treatment of liver tumors and prostate cancer has shown promise as a potential alternative to conventional therapies [4,5]. HIFU requires precise localization of the treatment area, and thus, it relies on imaging guidance. To support accurate treatment and avoid undesired damage to normal tissue, magnetic resonance imaging (MRI) guidance has been widely utilized [6]. However, MRI-guided HIFU often suffers from a long interval between MRI and HIFU application [7]. Thus, limited methods exist for tracking the ongoing process of disease treatment and adjusting the HIFU dosage in real time [8].
Ultrasound-guided HIFU was introduced to overcome this limitation. Ultrasound as a real-time imaging modality can manage the HIFU dosage and adjust the location of ablation during treatment [9]. However, the simultaneous application of ultrasound for both HIFU treatment and imaging guidance is not typically feasible because of their mutual interference. HIFU pulses create strong fundamental and harmonic signals that can impede ultrasound imaging, because the frequency range of the HIFU signals can overlap with the imaging frequencies [10].
To address this challenge, Song et al. [11] introduced a pulse-inversion–based HIFU treatment approach. In their method, two HIFU pulses with opposite phases are sequentially transmitted. Then, the received signals of each pulse are summed to cancel the fundamental and odd harmonics of HIFU interference. Thus, they were able to obtain HIFU-interference–free ultrasound images, from which odd HIFU harmonic signals had been removed. However, if two opposite phases of the HIFU signals are long, their interference cancellation may become less effective because of motion-induced phase differences. As an alternative approach, Jeong et al. [12] suggested adaptive notch filtering to remove unwanted HIFU signals from imaging signals. Because of the harmonics generated by the HIFU beams, the HIFU interference signals appear at multiples of the fundamental HIFU frequency. Therefore, it is possible to remove specific, harmonic HIFU frequency components using a notch filter. Lastly, Vaezy et al. [13] synchronously divided the HIFU transmission and the guidance imaging process to avoid their interference. However, their approach is less applicable when long, continuous HIFU treatment is required. More recently, singular value decomposition (SVD)–based blood flow imaging during HIFU exposure was suggested [14], which showed promising potential for eliminating HIFU artifacts from Doppler sequences.
For pulse-echo ultrasound imaging, an ultrasound transducer transmits a pulsed wave and receives the associated echo from human tissue to form a diagnostic ultrasound image. When the ultrasound image is reconstructed through the same process during HIFU treatment, the ultrasound images are substantially distorted, because the HIFU interference signal is more dominant than the ultrasound image signal. In general, the duration of the HIFU pulse is much longer than that of the ultrasound image pulse, and thus, the narrow-banded HIFU signals and their harmonics spectrally overlap within the bandwidth of the ultrasound image signal. Moreover, the magnitude of the therapeutic HIFU interference is much higher than that of diagnostic image signals [11]. Thus, the monitoring image is substantially distorted by the strong HIFU interference. The hypothesis of this study was that proper decomposition of ultrasound image signals would make it possible to selectively remove the specific components with strong HIFU interference, and thus, to obtain an interference-free image. This paper introduces an adaptive HIFU-interference filtering method that enables the simultaneous acquisition of ultrasound images during the HIFU treatment. This approach relies on SVD, which decomposes individual scanline data into several components, making it possible to extract interference-free ultrasound images by adaptively tracking the HIFU center frequencies [15,16]. Compared to the previous approach [14], decomposing two-dimensional (2-D) image data to select the desired components excluding HIFU signals, this approach relies on one-dimensional (1-D) scanline data to generate a sufficient number of decomposed components. In addition, harmonic imaging is used as a baseline imaging method to improve the contrast resolution of guidance images for effective lesion localization [17,18].

Materials and Methods

Theory of SVD

SVD is widely applied in signal processing to analyze real or complex matrices [14]. The SVD of an m×n matrix S can be formulated as
where is an m×n diagonal matrix, and U and V are m×m and n×n orthonormal matrices, respectively. The operator * in Eq. (1) presents the conjugate transpose. From Eq. (1), the matrix S can be decomposed as
where σi is the ith singular value, which is a diagonal element of , and the ith column of U and V are referred to as the left singular vector ui and right singular vector vi, respectively. Ai is the ith component of S decomposed by SVD. As these decomposed components contain independent features of the signals, each component can be selectively taken to exclude undesired characteristics in the signals.

Adaptive SVD Filtering

Post-beamformed data containing both ultrasound image signals and HIFU interference is first demodulated to be the baseband signals, as shown in Fig. 1. Before singular value decomposition, the 1-D analytic scanline data is re-arranged into the form of a 2-D Hankel matrix, as shown in Fig. 2. The transformed 2-D Hankel matrix is then decomposed into several 2-D components using the SVD. Each decomposed component is re-arranged back to the 1-D data through the inverse process of the Hankel matrix, as presented in Fig. 2. To construct the Hankel matrix from the individual scanline data, P and N were set to be 480 and 960, respectively, in this study.
From each 1-D component, the mean central frequency of the data is calculated based on the 1-D auto-correlation approach using Eq. (3). In the following process, the estimated mean frequency values are used to determine whether the data is a HIFU interference candidate to be removed.
where fmean(i) is the mean frequency of the ith decomposed 1-D array of the SVD component, fs is the sampling frequency of the received data, N is the number of samples in the scanline, and xi(n) presents the nth element signal of the ith 1-D array SVD component. For this study, the number of scanlines and the number of samples before demodulation were 128 and 1,920, respectively. The baseband data had 960 samples after decimation.
To preserve the image signals mixed within the HIFU frequency band, a tunable parameter defined as an attenuation factor (αk) is used, where k is the harmonic order of HIFU signals. For example, k of 1 indicates the fundamental frequency and k of 2, 3, … are the second and third harmonics, and so on. The attenuation factor αk determines the amount of HIFU fundamental and harmonic components that must be removed from the decomposed singular value components.
Eq. (4) finally classifies a set of HIFU interference components to be removed. fHIFU is the fundamental center frequency of the HIFU signal, fc is the center frequency of the ultrasound image signal, and αk is the attenuation factor of the kth HIFU interference. fBW represents the bandwidth of the HIFU signals. The HIFU bandwidth was initially determined from the −3 dB operating frequency of the transducer measured by the manufacturer, which was tuned to be optimal in the experimental settings of this study. Eq. (4) searches for whether the signal of interest is placed within the HIFU frequency band and whether its singular value is greater than the attenuation factor. When both conditions are satisfied, the component is classified into the HIFU interference signal to be removed by simply excluding SVD components that are classified as HIFU signals prior to the inverse Hankel process. The interference-free ultrasound image can then be produced by adding the remaining components, excluding the undesired HIFU components. This process is repeated for all scan-lines to form a single frame of a 2-D ultrasound image.

Experimental Setup

Fig. 3 shows the overall setup for experimental validation. We imaged a custom-made polyacrylamide phantom using a Verasonics research platform (Vantage 128, Verasonics Inc., Kirkland, WA, USA) with a convex array transducer (C5-2v, Verasonics Inc.). The center frequency of the image pulse was 2 MHz. The HIFU transducer with the imaging transducer inserted (H-230, Sonic Concepts Inc., Bothell, WA, USA) was used for HIFU exposure. The custom-made phantom included pin and cyst targets to demonstrate the spatial resolution and contrast to investigate the capability of HIFU interference removal in images. To drive the HIFU transducer, a continuous wave signal with an amplitude of 300 mVpp at a frequency of 1.6 MHz generated from the function generator (AFG 3102, Tektronix Inc., Beaverton, OR, USA) was amplified with a 55-dB radiofrequency amplifier (ENI 1040L, Electronic Navigation Industries, Rochester, NY, USA). For image acquisition, we acquired post-HIFU ultrasound images right after the HIFU exposure was initiated to avoid lesion coagulation to focus on the effect of HIFU noise removal by comparing pre- and post-HIFU images with the same phantom conditions.
During HIFU application, pulse-inversion–based harmonic imaging sequences were used to acquire the data, as shown in Fig. 4. For clarification, HIFU exposure is monotonically applied with the same phase and frequency. The imaging sequence uses the pulse inversion approach with two opposite phases of transmit pulses without any synchronization between HIFU and imaging. From the harmonic imaging sequence, we reconstructed both fundamental and harmonic images to further demonstrate that harmonic imaging can be more suitable in imaging guidance of HIFU treatment.


HIFU Interference Classification

Fig. 5A shows the frequency spectrum of the analytic signal mixed with the HIFU interference and ultrasound image signal. It can be seen that the magnitude of the HIFU interference was 10 dB to 30 dB larger than that of the image signal. The frequency spectrum of each scanline component decomposed by the SVD and its associated mean frequency (solid orange lines) were estimated, as shown in Fig. 5B. As explained in the previous section, for each scanline component, the algorithm searched whether its mean frequency is included in the HIFU bandwidth. The attenuation factors were determined according to the magnitude of the interference signal, as presented in Fig. 6. In this study, the attenuation factors were manually selected, but as seen in Fig. 6, the magnitude of singular values seemed to be proportional to the HIFU energy, which could be used to fully automate the algorithm. Then, the scanline components, which had larger singular values than the attenuation factors, were detected. Finally, the components satisfying both conditions were excluded when inversing the Hankel matrix to generate an ultrasound image without HIFU interference.

Baseline Imaging Results with and without HIFU Interference

The baseline imaging results without HIFU interference are presented in Fig. 7 as a control. The fundamental image was reconstructed from the signal centered at 2 MHz. For harmonic imaging, the pulse-inversion technique led to the center frequency doubling at 4 MHz. As shown in Fig. 7A, the resolution of three pin targets and the contrast of the cyst targets visually improved, and the reverberation clutter artifacts generated from the water tank were reduced in the harmonic image.
When the HIFU signal was concurrently applied with the guidance imaging, the reconstructed ultrasound images were substantially degraded by the HIFU interference. As a result, the pin targets, cysts, and background speckles from the phantom were nearly unobservable in both fundamental and harmonic images, as shown in Fig. 8. In addition, from the spectrum, the magnitudes of the HIFU fundamental and its harmonics were much higher than those of the ultrasound image signals, as shown in Fig. 8B.

Adaptive SVD-Based Filtering Results under HIFU Exposure

The imaging results processed by the proposed SVD-based filtering method to eliminate HIFU interference are shown in Fig. 9. The results were obtained from the same phantom as in Fig. 8, demonstrating that the HIFU distortion was effectively removed, as compared to the images without HIFU interference presented in Fig. 7. The corresponding frequency spectrum also confirmed that the fundamental and harmonic components of the HIFU signals were nearly removed, as shown in Fig. 9B.
To quantitatively confirm the capability of HIFU noise reduction, we additionally evaluated the structural similarity index measurement (SSIM) [19] between the original and processed images for both fundamental and harmonic imaging cases. The SSIM values of fundamental and harmonic images were measured to be 0.96 and 0.97, respectively, for the entire region of the image, confirming that this approach effectively produced HIFU noise-removed images, although a few stripe patterns can be found in the processed images in Fig. 9A.


This study has experimentally demonstrated that our adaptive SVD-based filtering removed the HIFU interference effectively and that the contrast resolution of the interference-free harmonic image also improved over the fundamental image. The clutter artifacts in the harmonic images were reduced compared to the fundamental image (Fig. 9A). Therefore, adaptive SVD filtering can be used to remove unwanted HIFU-introduced distortions in the ultrasound guidance image obtained during the HIFU exposure, which enables accurate localization of the lesion receiving treatment in real-time.
Various parameters used in our adaptive SVD filtering, including the number of decomposed components, the size of the Hankel matrix, the trade-off between the processed quality, and the computational time, need to be further optimized for specific clinical needs. Moreover, since the harmonic image signal is weaker than the fundamental signal, the pulse-inversion–based harmonic imaging technique was applied, which may cause motion artifacts in dynamic organs. For reliable pulse-inversion–based harmonic imaging during HIFU application, it should also be noted that the HIFU energy needs to be stable for transmit/receive events of multiple imaging pulses. The authors’ ongoing in vivo preclinical study targeting uterine fibroid treatment will focus on the practical, clinical use of this technique.
This study introduced an adaptive SVD-based filtering approach to support real-time interference-free guidance during HIFU treatment. The imaging results indicate that this approach effectively removed interference while preserving the image quality under HIFU exposure. The findings also demonstrated that harmonic imaging could improve image quality over the fundamental images by a qualitative comparison. The proposed harmonic SVD filtering approach would be useful for clinical applications requiring real-time image guidance during HIFU treatment.


This work was supported by a grant from the Institute of Information & Communications Technology Planning & Evaluation (IITP), funded by the Korean government (MSIT) (No. 2022-0-00101, Development of an intelligent HIFU therapy system using highly functional real-time image guide and therapeutic effect monitoring based on ICT fusion).


Author Contributions

Conceptualization: Chung E, Yoon H, Song TK. Data acquisition: Lee H. Data analysis or interpretation: Lee H, Chung E, Yoon H, Song TK. Drafting of the manuscript: Lee H, Yoon H. Critical revision of the manuscript: Chung E, Yoon H, Song TK. Approval of the final version of the manuscript: all authors.

Conflict of Interest

Tai-kyong Song serves as Editor for the Ultrasonography, but has no role in the decision to publish this article. All remaining authors have declared no conflicts of interest.


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Block diagram of the adaptive singular value decomposition (SVD)–based high-frequency ultrasound (HIFU) interference filtering method.
Fig. 1
The process of rearranging the 1-D vector X into a 2-D Hankel matrix H.
The ith column of H is composed by arranging the ith to i+P−1th elements of X, where P is the column size of H. The inverse operation process calculates the average value of the reverse diagonal elements. 1-D, one-dimensional; 2-D, two-dimensional.
Fig. 2
Experimental setup to obtain ultrasound images under high-frequency ultrasound (HIFU) exposure.
The signal generated from the function generator is passed through the amplifier to apply the HIFU signal. The convex array transducer is placed in the middle opening part of the HIFU transducer. The customized phantom is positioned in the imaging plane. The HIFU experiment is conducted in de-gassed water, and real-time ultrasound data is acquired using a Verasonics system.
Fig. 3
High-frequency ultrasound (HIFU) and ultrasound imaging sequence.
During continuous HIFU application, the imaging transducer transmits and receives the pulses with phases of 0° and 180° to create a signal frame of a pulse-inversion ultrasound harmonic image, which is repeated to form the 2-D image data. HIFU, high-frequency ultrasound; 2-D, two-dimensional.
Fig. 4
Component analysis of the mixture signal in the frequency domain.
A. Frequency spectrum of the data mixed with high-frequency ultrasound (HIFU) interference (red arrow) and ultrasound image signal (green arrow). B. The spectrums and orange solid line represent the ith component’s frequency plot and its mean frequency decomposed by singular value decomposition (SVD), respectively.
Fig. 5
Spectrum and singular value plots for the attenuation factor.
A. Frequency spectrum of the mixture data is shown. The red region represents the high-frequency ultrasound (HIFU) bands. B. Singular value in the dB scale calculated from the singular value decomposition process. The attenuation factors were chosen based on the magnitude of the interference signal from each HIFU band.
Fig. 6
Baseline imaging results with no high-frequency ultrasound interference.
Ultrasound fundamental and harmonic images (A) with two arrows indicating a pin target of interest (left arrow) and a clutter signal (right arrow) for both fundamental and harmonic images, their corresponding frequency spectrum measured at the 64th scanline (B), and the demodulated baseband spectrum in B (C) are shown.
Fig. 7
Imaging results under high-frequency ultrasound exposure.
Ultrasound fundamental and harmonic images (A), their corresponding frequency spectrum measured at the 64th scanline (B), and the demodulated spectrum from the red region in B (C) are shown.
Fig. 8
Adaptive singular value decomposition–filtered imaging results under high-frequency ultrasound exposure.
Ultrasound fundamental and harmonic images (A) with three arrows indicating a pin target of interest (left arrow), a clutter signal (right arrow), and a hypoechoic cyst (bottom arrow) for both fundamental and harmonic images and their corresponding frequency spectrum measured at the 64th scanline (B) are shown.
Fig. 9
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