Designing waveforms for temporal encoding using a frequency sampling method

Investigation of Non-linear Chirp Coding for Improved Second Harmonic Pulse Compression

Non-linear frequency-modulated (NLFM) chirp coding was investigated to improve the pulse compression of the second harmonic chirp signal by reducing the range side lobe level. The problem of spectral overlap between the fundamental component and second harmonic component (SHC) was also investigated. Therefore, two methods were proposed: method I for the non-overlap condition and method II with the pulse inversion technique for the overlap harmonic condition. In both methods, the performance of the NLFM chirp was compared with that of the reference LFM chirp signals. Experiments were performed using a 2.25 MHz transducer mounted coaxially at a distance of 5 cm with a 1 mm hydrophone in a water tank, and the peak negative pressure of 300 kPa was set at the receiver. Both simulations and experimental results revealed that the peak side lobe level (PSL) of the compressed SHC of the NLFM chirp was improved by at least 13 dB in method I and 5 dB in method II when compared with the PSL of LFM chirps. Similarly, the integrated side lobe level (ISL) of the compressed SHC of the NLFM chirp was improved by at least 8 dB when compared with the ISL of LFM chirps. In both methods, the axial main lobe width of the compressed NLFM chirp was comparable to that of the LFM signals. The signal-to-noise ratio of the SHC of NLFM was improved by as much as 0.8 dB, when compared with the SHC of the LFM signal having the same energy level. The results also revealed the robustness of the NLFM chirp under a frequency-dependent attenuation of 0.5 dB/cm·MHz up to a penetration depth of 5 cm and a Doppler shift up to 12 kHz.

SARUS: A Synthetic Aperture Real-time Ultrasound System

The Synthetic Aperture Real-time Ultrasound System (SARUS) for acquiring and processing synthetic aperture (SA) data for research purposes is described. The specifications and design of the system are detailed, along with its performance for SA, nonlinear, and 3-D flow estimation imaging. SARUS acquires individual channel data simultaneously for up to 1024 transducer elements for a couple of heart beats, and is capable of transmitting any kind of excitation. The 64 boards in the system house 16 transmit and 16 receive channels each, where sampled channel data can be stored in 2 GB of RAM and processed using five field-programmable gate arrays (FPGAs). The fully parametric focusing unit calculates delays and apodization values in real time in 3-D space and can produce 350 million complex samples per channel per second for full non-recursive synthetic aperture B-mode imaging at roughly 30 high-resolution images/s. Both RF element data and beamformed data can be stored in the system for later storage and processing. The stored data can be transferred in parallel using the system's sixty-four 1-Gbit Ethernet interfaces at a theoretical rate of 3.2 GB/s to a 144-core Linux cluster.

Orthogonal quadratic chirp signals for simultaneous multi-zone focusing in medical ultrasound imaging

In medical ultrasound imaging, multi-zone focusing on transmission is used to enhance the lateral resolution at the expense of frame rate. As an alternative, this paper proposes a simultaneous multi-zone focusing method using orthogonal quadratic chirp signals to improve lateral resolution without sacrificing frame rate. In the proposed method, two weighted quadratic chirp signals with different spectra are simultaneously transmitted with different transmit time delays for multi-zone focusing. Because the two weighted quadratic chirps can be designed to have a desired level of cross-correlation after compression, the degradation of axial resolution resulting from the division of a spectrum is minimized. Through simulation, the performances of the proposed method were evaluated and compared with those of two-cycle pulsed excitation as a gold standard and two sub-band weighted linear chirps. In the simulation, the proposed method improved -6-dB and -20-dB lateral beam widths by factors of 1.67 and 1.84, respectively, compared with the pulsed excitation. The degradation of axial resolution in the proposed method was maximally 43% less than that in the linear chirp case. The results demonstrate that the proposed method is useful in the improvement of overall ultrasound image quality because the axial resolution of conventional ultrasound images is generally a few times higher than the lateral resolution.

Pulse compression of harmonic chirp signals using the fractional fourier transform

In ultrasound harmonic imaging with chirp-coded excitation, a harmonic matched filter (HMF) is typically used on the received signal to perform pulse compression of the second harmonic component (SHC) to recover signal axial resolution. Designing the HMF for the compression of the SHC is a problematic issue because it requires optimal window selection. In the compressed second harmonic signal, the sidelobe level may increase and the mainlobe width (MLW) widen under a mismatched condition, resulting in loss of axial resolution. We propose the use of the fractional Fourier transform (FrFT) as an alternative tool to perform compression of the chirp-coded SHC generated as a result of the nonlinear propagation of an ultrasound signal. Two methods are used to experimentally assess the performance benefits of the FrFT technique over the HMF techniques. The first method uses chirp excitation with central frequency of 2.25 MHz and bandwidth of 1 MHz. The second method uses chirp excitation with pulse inversion to increase the bandwidth to 2 MHz. In this study, experiments were performed in a water tank with a single-element transducer mounted coaxially with a hydrophone in a pitch-catch configuration. Results are presented that indicate that the FrFT can perform pulse compression of the second harmonic chirp component, with a 14% reduction in the MLW of the compressed signal when compared with the HMF. Also, the FrFT provides at least 23% reduction in the MLW of the compressed signal when compared with the harmonic mismatched filter (HMMF). The FrFT maintains comparable peak and integrated sidelobe levels when compared with the HMF and HMMF techniques.

Segmented motion compensation for complementary coded ultrasonic imaging

Ultrasonic imaging using complementary coded pulses offers the SNR improvements of signal coding without the filter side-lobes introduced by single-transmit codes. Tissue motion between coded pulse emissions, however, can introduce high side-lobes caused by misalignment of complementary filter outputs. This paper presents a method for filtering and motion compensation of complementary coded signals appropriate for use in medical imaging. The method is robust to the effects of non-ideal transducers on the imaging signals, includes mirrored compensation stages to reduce the impact of motion estimation error, and has been shown to reduce side-lobes to levels that compare favorably to systems using FM-coded signals of similar length and bandwidth while providing increased coding gain and range resolution. In addition, motion compensation allows the received data to be used without the frame-rate penalty usually incurred by complementary-coded imaging. The method has been verified using simulated point and speckle targets with both homogeneous and inhomogeneous motion profiles. Selected results have been verified experimentally.

Precise time-of-flight calculation for 3-D synthetic aperture focusing

Conventional linear arrays can be used for 3-D ultrasound imaging by moving the array in the elevation direction and stacking the planes in a volume. The point-spread function is larger in the elevation plane, because the aperture is smaller and has a fixed elevation focus. Resolution improvements in elevation can be achieved by applying synthetic aperture focusing to the beamformed-in-plane RF data. The proposed method uses a virtual source placed at the elevation focus for postbeamforming. This has previously been done in 2 steps, in-plane focusing followed by synthetic aperture postfocusing in elevation, due to lack of a simple expression for the exact time of flight. This paper presents a new single step method for calculating the time of flight for a 3-D case using a linear array. The new method is more flexible and is able to beamform a fewer number of points much more efficiently. The method is evaluated using both simulated data and phantom measurements using the RASMUS experimental scanner. Computational cost of the method is higher than the 2-step method for a full volume beamforming, but it allows for a reduction of an order-of-magnitude if 3 planes are used for real-time visualization. In addition, the need for a temporary storage of beamformed data is removed.

Coded ultrasound for blood flow estimation using subband processing

This paper investigates the use of coded excitation for blood flow estimation in medical ultrasound. Traditional autocorrelation estimators use narrow-band excitation signals to provide sufficient signal-to-noise-ratio (SNR) and velocity estimation performance. In this paper, broadband coded signals are used to increase SNR, followed by subband processing. The received broadband signal is filtered using a set of narrow-band filters. Estimating the velocity in each of the bands and averaging the results yields better performance compared with what would be possible when transmitting a narrow-band pulse directly. Also, the spatial resolution of the narrow-band pulse would be too poor for brightness-mode (B-mode) imaging, and additional transmissions would be required to update the B-mode image. For the described approach in the paper, there is no need for additional transmissions, because the excitation signal is broadband and has good spatial resolution after pulse compression. This means that time can be saved by using the same data for B-mode imaging and blood flow estimation. Two different coding schemes are used in this paper, Barker codes and Golay codes. The performance of the codes for velocity estimation is compared with a conventional approach transmitting a narrow-band pulse. The study was carried out using an experimental ultrasound scanner and a commercial linear array 7 MHz transducer. A circulating flow rig was scanned with a beam-to-flow angle of 60 degrees. The flow in the rig was laminar and had a parabolic flow-profile with a peak velocity of 0.09 m/s. The mean relative standard deviation of the velocity estimate using the reference method with an 8-cycle excitation pulse at 7 MHz was 0.544% compared with the peak velocity in the rig. Two Barker codes were tested with a length of 5 and 13 bits, respectively. The corresponding mean relative standard deviations were 0.367% and 0.310%, respectively. For the Golay coded experiment, two 8-bit codes were used, and the mean relative standard deviation was 0.335%.

High frame-rate blood vector velocity imaging using plane waves: simulations and preliminary experiments

Conventional ultrasound methods for acquiring color images of blood velocity are limited by a relatively low frame-rate and are restricted to give velocity estimates along the ultrasound beam direction only. To circumvent these limitations, the method presented in this paper uses 3 techniques: 1) The ultrasound is not focused during the transmissions of the ultrasound signals; 2) A 13-bit Barker code is transmitted simultaneously from each transducer element; and 3) The 2-D vector velocity of the blood is estimated using 2-D cross-correlation. A parameter study was performed using the Field II program, and performance of the method was investigated when a virtual blood vessel was scanned by a linear array transducer. An improved parameter set for the method was identified from the parameter study, and a flow rig measurement was performed using the same improved setup as in the simulations. Finally, the common carotid artery of a healthy male was scanned with a scan sequence that satisfies the limits set by the Food and Drug Administration. Vector velocity images were obtained with a frame-rate of 100 Hz where 40 speckle images are used for each vector velocity image. It was found that the blood flow approximately followed the vessel wall, and that maximum velocity was approximately 1 m/s, which is a normal value for a healthy person. To further evaluate the method, the test person was scanned with magnetic resonance (MR) angiography. The volume flow derived from the MR scanning was compared with that from the ultrasound scanning. A deviation of 9% between the 2 volume flow estimates was found.