Orthogonal Golay excitation for range side lobe elimination in dual-frequency harmonic imaging

https://doi.org/10.1016/j.bspc.2015.02.013Get rights and content

Highlights

  • Dual-frequency harmonic imaging benefits from improvement of SNR by Golay excitation.

  • Conventional Golay decoding suffers from spectral crosstalk with 3f0 and DC interferences.

  • For orthogonal Golay, the output of exchanged filtering can be subtracted from that of the original filtering to remove the crosstalk.

  • Results demonstrate the reduction of range side lobe level in both hydrophone measurement and B-mode imaging.

Abstract

Dual-frequency (DF) tissue harmonic imaging has been developed to take advantage of not only harmonic signal at second harmonic (2f0) frequency but also the inter-modulation harmonic signal at fundamental (f0) frequency for simultaneous nonlinear detection. Though phase-encoded Golay pair can improve the signal-to-noise ratio of DF harmonic signal at both f0 and 2f0 frequencies, conventional matched filtering cannot correctly decode the crosstalk from harmonic components at DC and third harmonic (3f0) frequency and will lead to range side lobe artifacts in DF harmonic imaging. For orthogonal Golay pair, however, exchanging the decoding filter will output zero for the signal and keep the crosstalk the same. Therefore, the output of exchanged filtering can be subtracted from that of the original matched filtering to completely remove the spectral crosstalk. Compared to phase inversion method, the proposed orthogonal Golay decoding does not require additional transmits to cancel the unwanted DC and 3f0 harmonic interferences and thus the achievable frame rate remains the same. Various experiments have been performed to verify the efficacy of the proposed orthogonal Golay decoding. Results from hydrophone measurements indicate that the proposed method effectively suppresses the spectral overlap between the harmonic signal and the interference. Corresponding range side lobe level (RSLL) can be suppressed by 10–20 dB when the signal bandwidth is 60%. B-mode harmonic imaging also demonstrates a reduction of side lobe magnitude (SLM) by 8 dB at 2f0 frequencies.

Introduction

Conventionally, tissue harmonic imaging relies on the received nonlinear signal at second harmonic (2f0) frequency to construct the image and thus only the transmission at fundamental (f0) frequency is required [1], [2]. Since both transmission and reception are single-frequency (SF), the conventional method does not fully exploit the available system bandwidth. In order to fully utilize the system bandwidth, dual-frequency (DF) harmonic imaging has been proposed to provide simultaneous nonlinear detection of imaged objects at two distinct frequencies [3], [4], [5]. DF transmit waveform comprises of both f0 and 2f0 components to produce not only the self coupling of the f0 component but also the mutual coupling between the f0 and 2f0 components. Consequently, the received harmonic signal for DF imaging contains both the second harmonic component at 2f0 frequency and the inter-modulation component at f0 frequency. Since the two harmonic components are simultaneously available, they can be further spectrally compounded to improve the image contrast. Specifically, the spectral compounding is performed by combining the original 2f0 harmonic signal envelope with the additional f0 harmonic signal envelope to smooth the speckle variation. Note that the DF harmonic image with spectral compounding will have the same axial resolution as the SF counterpart [5].

However, DF harmonic imaging still suffers from the intrinsic limitation of low signal-to-noise ratio (SNR). By utilizing elongated transmit waveform with low transmit amplitude, coded excitation delivers more acoustic energy into tissue to boost harmonic generation while still complying with safety regulations on acoustic output [6], [7], [8], [9], [10]. When the echoes from elongated transmit are received, a decoding filter is used to compress the acoustic energy into a short time interval to restore the axial resolution. For frequency encoding, the frequency-modulated waveform comprising of a sinusoid with sweeping instantaneous frequency such as the chirp waveform is commonly adopted. For phase encoding, on the other hand, the phase modulation is performed by changing the phase in a binary bit sequence such as in the Barker sequence and the Golay sequence. Among these phase codes, the Golay sequence can provide complete elimination of the range side lobes after compression by using a pair of complementary code [6]. Therefore, the Golay sequence is selected as an example of phase-encoded waveform in this study.

As indicated in Eq. (1), a pair of N-bit binary sequences A(n) and B(n) (n = 1, …, N) is complementary Golay when the sum of their respective matched filtering is a delta function with 2N magnitude:A(n)*A(n)+B(n)*B(n)=2Nδ(n)where * represents the convolution, N is the number of bits and δ(n) represents the delta function. Eq. (1) also indicates that the N-bit Golay sequence can be temporally compressed to a 1-bit delta function without the presence of any range side lobe in ultrasound imaging. For a 2-bit Golay, the decoding process can be schematically illustrated in Fig. 1(a) with A = [1 −1] and B = [−1 −1]. Note that the 2-bit Golay sequences are also orthogonal to each other. Specifically, when the decoding filters for the A and B sequence in Eq. (1) are exchanged, the sum of their respective filtering is zero as shown in Fig. 1(b):A(n)*B(n)+B(n)*A(n)=0

For any pair of sequence satisfying both Eqs. (1), (2), it is referred to as the orthogonal Golay pair. In this study, the orthogonal property of Golay pair is utilized to suppress the range side lobe artifacts from potential spectral crosstalk in DF harmonic imaging. It should be noted that, when the imaged object moves, the range side lobes of the Golay pair are no longer completely canceled in Eq. (1) and the orthogonal property in Eq. (2) is also compromised. This may produce side lobe artifacts that blur the image. Therefore, application of Golay excitation is generally limited to quasi-stationary tissue in ultrasound imaging [11]. Otherwise, motion compensation may be required to alleviate the range side lobe artifacts at the cost of extensive computation [12].

Section snippets

Golay excitation in DF harmonic imaging

In DF harmonic imaging, the transmit waveform comprises the f0 and 2f0 transmit components:x(t)=[cos(2πf0t+(θ1))+cos(2π(2f0)t+(θ2))]

In Eq. (3), θ1 and θ2 are the transmit phases at f0 frequency and 2f0 frequency, respectively. Generally, the f0 component is allocated in the lower side band of the transducer while the 2f0 component is in the upper side band to provide adequate sensitivity at both frequencies. As in Eq. (4), the resultant second-order harmonic signal can be modeled by the square

Experimental setup

Hydrophone measurements are first performed to validate the efficacy of orthogonal Golay decoding. The experimental system for hydrophone measurements comprises one 3.5-MHz single-element transmit transducer with a −6-dB fractional bandwidth of 80% (Panametrics V380, Waltham, MA, U.S.A.) and one calibrated PVDF needle hydrophone (Force Technology, MH28-6, Brøndby, Denmark) in a water tank. The Golay sequences are generated by an arbitrary function generator (model 2571, Tabor Electronics, Tel

Results

Fig. 4(a–d) shows the PI harmonic spectra in the hydrophone measurements, respectively with signal bandwidths of 30%, 40%, 50% and 60%. Either original Golay decoding or orthogonal Golay decoding has been performed for comparison. With original Golay decoding, the harmonic signal is present at not only imaging bands (i.e. f0 and 2f0) but also the interference bands (i.e. DC and 3f0). Note that the imaging signals at f0 and 2f0 bands have been successfully decoded to [0 4 0] as shown in Fig. 3

Discussions and concluding remarks

In DF harmonic imaging, the second-order harmonic components at f0 and 2f0 frequencies are simultaneously generated and can be spectrally compounded to suppress image speckle. However, when Golay excitation is utilized to improve harmonic SNR, crosstalk from DC and 3f0 harmonic components could produce range side lobe in the decoding process of the f0 and 2f0 harmonic components. Note that the amount of spectral overlap between the imaging bands (i.e., f0 and 2f0) and the interference bands

Acknowledgments

This work was supported by the Ministry of Science and Technology of Taiwan under Grant No. 102-2628-B-011-001-MY3 and National Taiwan University of Science and Technology and Mackay Memorial Hospital of Taiwan under Grant No. MMH-NTUST-103-03.

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