The high frame rate (HFR) imaging technique requires only one emission event for imaging. Therefore, it can achieve ultrafast imaging with frame rates up to the kHz regime, which satisfies the frame rate requirements for imaging moving tissues in scientific research and clinics. Lu’s Fourier migration method is based on a non-diffraction beam to obtain HFR images and can improve computational speed and efficiency. However, in order to obtain high-quality images, Fourier migration needs to make full use of the spectrum of echo signals for imaging, which requires a large number of Fast Fourier Transform (FFT) points and increases the complexity of the hardware when the echo frequency is high. Here, an efficient algorithm using the spectrum migration technique based on the spectrum’s distribution characteristics is proposed to improve the imaging efficiency in HFR imaging. Since the actual echo signal spectrum is of limited bandwidth, low-frequency and high-frequency parts with low-energy have little contribution to the imaging spectrum. We transform the effective part that provides the main energy in the signal spectrum to the imaging spectrum while the ineffective spectrum components are not utilized for imaging. This can significantly reduce the number of Fourier transform points, improve Fourier imaging efficiency, and ensure the imaging quality. The proposed method is evaluated on simulated and experimental datasets. Results demonstrated that the proposed method could achieve equivalent image quality with a reduced point number for FFT compared to the complete spectrum migration. In this paper, it only requires a quarter of the FFT points used in the complete spectrum migration, which can improve the computational efficiency; thus, it is more suitable for real-time data processing. The proposed spectrum migration method has a specific significance for the study and clinical application of HFR imaging.

Studies on non-diffraction-based imaging emit a non-diffraction wave-field and have been described since the 1990s [

To improve the imaging quality of HFR, two kinds of methods for resolution enhancements in HFR imaging have been proposed by Cheng et al. [

In the study of Chen et al. [

Zhao et al. [

In the HFR imaging system based on Fourier transform, FFT technique is a core part to realize HFR imaging. Although many studies are developed to improve the quality of HFR imaging, there are few researches aim to reduce the number of FFT points and improve the efficiency of the FFT operation. Since the spectrum of practical signals has a limited bandwidth, not all frequency points in the spectrum are needed to calculate FFT when transforming the echo signal spectrum to the imaging spectrum in Fourier migration. This paper proposes an imaging method using a spectrum migration technique that ignores the low-frequency and high-frequency parts with low-energy to improve the computational efficiency of FFT. The imaging spectrum is migrated from the high-frequency region to the low-frequency region so that the signal spectrum can be fully utilized. This method only migrates the most concentrated part of the spectrum energy in the signal to the imaging spectrum area, thus it ensures image quality and reduces the number of FFT points. The results indicate that the spectrum migration method effectively reduces the number of FFT points and improve the FFT transformation efficiency. It also reduces the influence of side lobes on imaging quality and improves imaging quality in resolution and contrast.

First, the acoustic field of the impulse plane wave _{j}

The echo signals received from scattering points in the plane _{j}

where

Due to the reflection of scattering targets, echoes represented by

In reality, echo signals are received from many planes in the acoustic field, and thus the received signal should be the integral of

The received signal, after a simple mathematical processing using

where

The

We assume

Considering the effect of signal bandwidth, the HFR imaging results can be approximately obtained by inverse Fourier transformation of the spectrum

where

The imaging process of HFR imaging systems rely on FFT, which has an advantage of high computational efficiency. However, in practical applications, the utilization rate of the high frequency signals spectrum is usually low.

We analyze the imaging model corresponding to _{y}

During imaging, the ultrasonic propagation is in the direction of +z. Therefore, the values of _{z}_{x}

According to the data provided by the Plane-wave Imaging Challenge in Medical Ultrasound (PICMUS) [

Due to the limited spectrum range of ultrasonic signals, the spectrum components in the low frequency (lower than _{c1}) and the high frequency (higher than _{c2}) are approximately zero (_{0}. Areas _{c1}) and the high frequency (higher than _{c2}) in _{0}; it ranges from _{c1} to _{c2}. When the frequency of ultrasonic signal is high, the imaging spectrum distribution moves to region

Due to the limitations of the FFT points, the high frequency spectrum is not effectively utilized for imaging. Therefore, we adopt spectrum migration to move the imaging spectrum from high frequency to low frequency–-this approach not only fills the low frequency gap of the imaging spectrum but also moves the spectrum region of high frequency to the effective region required by FFT. Thus, the spectrum of the signal can be fully utilized. The wave number

Here, _{c}_{c}_{c}

After spectrum migration, the most concentrated part of the spectrum component of the signal, namely the main lobe, can be used to generate the spectrum of the image. Obviously, this migration maximizes the utilization rate of the spectrum of the signal.

Thus, according to

where

The solution to

The spectrum migration method was tested using data sets provided by the PICMUS organized by the IEEE International Ultrasonics Symposium (IUS). Simulated and experimental data sets contain 75 plane waves covering a

The simulated data set constitutes horizontally distributed and vertically distributed point targets.

The spectrum of the echo signal mainly ranges from 2 to 8 MHz; thus, the corresponding imaging spectrum range is 16.3–65.2 radians/mm. In the simulation, the image size is

There was massive cyst tissue and several point targets in standard ultrasonic phantom. The echo signal was acquired by a Vantage 256 transducer and an open multi-channel ultrasonic research platform produced by the Verasonics Corporation of the US.

The experimental results are given in

In Jensen’s study [

In both simulation and experiment, the transducer size is 38.4 mm, and the imaging depth is 76.8 mm. According to

When the FFT points _{c}_{c}

For two-dimensional

Method | Number of FFT points | Spectrum utilization | Image quality | Computational complexity |
---|---|---|---|---|

Fourier migration | Partial spectrum | Low | Low | |

Fourier migration | Complete spectrum | High | High | |

Spectrum migration | Main spectrum | High | Low |

This work presents an HFR imaging method using the spectrum migration technique. Considering that the echo signal is a bandwidth signal, the signal spectrum with a large energy contributes the most to the imaging spectrum while the part outside the effective spectrum with less energy has a smaller contribution to the imaging spectrum. Therefore, the proposed method ignores the less energy of the spectrum when converting the signal spectrum to the imaging spectrum; it only migrates the effective signal spectrum to the low-frequency region. This can effectively reduce the number of FFT transform points in the imaging process and improve the computational efficiency. Besides, the proposed method migrates the most concentrated part of the spectrum energy to the imaging spectrum region to guarantee high image quality. Results indicate that the spectrum migration method effectively improves the quality and computational efficiency of HFR imaging.

The authors are grateful to the PICMUS organizers for sharing imaging data.