Compressed Sensing Based Synthetic Transmit Aperture for Phased Array Using Hadamard Encoded Diverging Wave Transmissions

Deep Null Space Learning Improves Dataset Recovery for High Frame Rate Synthetic Transmit Aperture Imaging

Synthetic transmit aperture (STA) imaging benefits from the two-way dynamic focusing to achieve optimal lateral resolution and contrast resolution in the full field of view, at the cost of low frame rate (FR) and low signal-to-noise ratio (SNR). In our previous studies, compressed sensing-based STA (CS-STA) and minimal ${l}_{{2}}$ -norm least squares (LS-STA) methods were proposed to recover the complete STA dataset from fewer Hadamard-encoded (HE) plane wave (PW) transmissions. Results demonstrated that, compared with STA imaging, CS/LS-STA can maintain the high resolution of STA in the full field of view and improve the contrast in the deep region with increased FR. However, these methods would introduce errors to the recovered STA datasets and subsequently produce severe artifacts to the beamformed images, especially in the shallow region. Recently, we discovered that the theoretical explanation for the error introduced in the LS-STA-based recovery is that the LS-STA method neglects the null space component of the real STA dataset. To deal with this problem, we propose to train a convolutional neural network under the null space learning framework (CNN-Null) to estimate the missing null space component) for high-accuracy recovery of the STA dataset from fewer HE PW transmissions. The mapping between the low-quality STA dataset (i.e., the range space component of the real STA dataset recovered using the LS-STA method) and the missing null space component of the real STA dataset was learned by the network with the high-quality STA dataset (obtained using full HE STA (HE-STA) imaging) as training labels. The performance of the proposed CNN-Null method was compared with the baseline LS-STA, conventional STA, and HE-STA methods, in terms of the visual quality, the normalized root mean square error (NRMSE), the generalized contrast-to-noise ratio (gCNR), and the lateral full-width at half-maximum (FWHM). The results demonstrate that the proposed method can greatly improve the recovery accuracy of the STA datasets (lower NRMSE) and, therefore, effectively suppress the artifacts presented in the images (especially in the shallow region) obtained using the LS-STA method (with a gCNR improvement of 0.4 in the cross-sectional carotid artery images). In addition, the proposed method can maintain the high lateral resolution of STA with fewer (as low as 16) PW transmissions, as LS-STA does.

Comparison of Spatial Encodings for Ultrasound Imaging

Ultrasound pulse sequencing and receive signal focusing work hand-in-hand to determine image quality. These are commonly linked by geometry, for example, using focused beams or plane waves in transmission paired with appropriate time-of-flight calculations for focusing. Spatial encoding allows a broader class of array transmissions but requires decoding of the recorded echoes before geometric focusing can be applied. Recent work has expanded spatial encoding to include not only element apodizations, but also element time delays. This powerful technique allows for a unified beamforming strategy across different pulse sequences and increased flexibility in array signal processing giving access to estimates of individual transmit element signals, but tradeoffs in image quality between these encodings have not been previously studied. We evaluate in simulation several commonly used time delay and amplitude encodings and investigate the optimization of the parameter space for each. Using the signal-to-noise ratio (SNR), point resolution, and lesion detectability, we found tradeoffs between focused beams, plane waves, and Hadamard weight encodings. Beams with broader geometries maintained a wider field of view after decoding at the cost of the SNR and lesion detectability. Focused beams and plane waves showed slightly reduced resolution compared to Hadamard weights in some cases, especially close to the array. We also found overall degraded image quality using random weight or random delay encodings. We validate these findings with experimental phantom imaging for select cases. We believe that these findings provide a starting point for sequence optimization and improved image quality using the spatial encoding approach for imaging.

Partial Hadamard encoded synthetic transmit aperture for high frame rate imaging with minimall2-norm least squares method

Objective.Synthetic transmit aperture (STA) ultrasound imaging is well known for ideal focusing in the full field of view. However, it suffers from low signal-to-noise ratio (SNR) and low frame rate, because each transducer element must be activated individually. In our previous study, we encoded all the transducer elements with partial Hadamard matrix and reconstructed the complete STA dataset with compressed sensing (CS) algorithm (CS-STA). As all the elements are activated in each transmission and the number of transmissions is smaller than that of STA, this method can achieve higher SNR and higher frame rate. Its main drawback is the time-consuming CS reconstruction (∼hours). In this study, we propose to accelerate the complete STA dataset reconstruction with minimall₂-norm least squares method.Approach.Partial Hadamard apodized plane wave (PW) transmissions were performed to acquire the PW dataset. Thereafter, the complete STA dataset can be reconstructed from the PW dataset with minimall₂-norm least squares method. Due to the orthogonality of partial Hadamard matrix, the minimall₂-norm least squares solution can be easily calculated.Main results.The proposed method is tested with simulation data and experimental phantom andin-vivodata. The results demonstrate that the proposed method achieves ∼5 × 10³times faster reconstruction speed than CS algorithm. The simulation results demonstrate that the proposed method is capable of achieving the same accuracy as the conventional CS-STA method for the STA dataset reconstruction. The simulations, phantom andin-vivoexperiments show that the proposed method is capable of improving the generalized contrast-to-noise ratio (gCNR) and SNR with maintained spatial resolution and fewer transmissions, compared with STA.Significance.In conclusion, the improved image quality and reduced computational time of LS-STA pave the way for its real-time applications in the clinics.

Acceleration of reconstruction for compressed sensing based synthetic transmit aperture imaging by using in-phase/quadrature data

Compressed sensing-based synthetic transmit aperture (CS-STA) was previously proposed to recover the full radio-frequency (RF) channel dataset of synthetic transmit aperture (STA) from that of a smaller number of randomly apodized plane wave (PW) transmissions. In this way, the imaging frame rate (FR) and contrast are improved with maintained spatial resolution, compared with those of STA. Because CS-STA reconstruction is repeated for all receive elements and RF samples (with a high sampling frequency), the recovery of STA dataset in RF domain is time-consuming. In the meantime, a large amount of RF data needs to be transferred and stored, resulting in an increase of system complexity and required memory space. In this study, CS-STA is extended to in-phase/quadrature (IQ) domain (with lower sampling frequency) for the recovery of baseband STA IQ dataset to accelerate the CS-STA reconstruction by reducing the amount of data to be processed. More importantly, CS-STA reconstruction using IQ data is of practical importance, as clinical ultrasound systems typically record baseband IQ signal instead of RF signal. Simulations, phantom and in vivo experiments verify the feasibility of CS-STA in IQ domain for the recovery of STA dataset. More specifically, CS-STA using IQ data achieves similar image quality and appreciably improves reconstruction speed (by ∼3 times) compared with that using RF data. These findings demonstrate that IQ-domain CS-STA is capable of relieving the computational and storage burdens, which may facilitate the implementation of CS-STA in practical ultrasound systems.

ApodNet: Learning for High Frame Rate Synthetic Transmit Aperture Ultrasound Imaging

Two-way dynamic focusing in synthetic transmit aperture (STA) beamforming can benefit high-quality ultrasound imaging with higher lateral spatial resolution and contrast resolution. However, STA requires the complete dataset for beamforming in a relatively low frame rate and transmit power. This paper proposes a deep-learning architecture to achieve high frame rate STA imaging with two-way dynamic focusing. The network consists of an encoder and a joint decoder. The encoder trains a set of binary weights as the apodizations of the high-frame-rate plane wave transmissions. In this respect, we term our network ApodNet. The decoder can recover the complete dataset from the acquired channel data to achieve dynamic transmit focusing. We evaluate the proposed method by simulations at different levels of noise and in-vivo experiments on the human biceps brachii and common carotid artery. The experimental results demonstrate that ApodNet provides a promising strategy for high frame rate STA imaging, obtaining comparable lateral resolution and contrast resolution with four-times higher frame rate than conventional STA imaging in the in-vivo experiments. Particularly, ApodNet improves contrast resolution of the hypoechoic targets with much shorter computational time when compared with other high-frame-rate methods in both simulations and in-vivo experiments.

Towards practical implementation of the compressed sensing framework for multi-element synthetic transmit aperture imaging

Compressed sensing (CS) has been adapted to synthetic aperture (SA) ultrasound imaging to improve the frame-rate of the system. Recently, we proposed a novel CS framework using Gaussian under-sampling to reduce the number of receive elements in multi-element synthetic transmit aperture (MSTA) imaging. However, that framework requires different receive elements to be chosen randomly for each transmission, which may add to practical implementation challenges. Modifying the scheme to employ the same set of receive elements for all transmissions of MSTA leads to degradation of the recovered image quality. Therefore, this work proposes a novel sampling scheme based on a genetic algorithm (GA), which optimally chooses the receive element positions once and uses it for all the transmission of MSTA. The CS performance using GA sampling schemes is evaluated against the previously proposed CS framework on in-vitro and in-vivo datasets. The obtained results suggest that not only does the GA-based approach allows the use of the same set of sparse receive elements for each transmit, but also leads to the lowest CS recovery error (NRMSE) and 14% overall improvement in image contrast, in comparison to the previously-proposed Gaussian sampling scheme. Thus, using the CS framework along with GA, can potentially reduce the complexity in implementation of CS-framework to MSTA based systems.

Ultrafast Phased-Array Imaging Using Sparse Orthogonal Diverging Waves

We present a new transmit pulse encoding scheme for ultrafast phased-array imaging called sparse orthogonal diverging wave imaging (SODWI). In SODWI, Hadamard encoding is used to selectively invert transmit pulse phases beamformed with a diverging wave delay profile. This approach has the advantage of delivering energy to a much wider field of view than conventional Hadamard-encoded multielement synthetic transmit aperture (HMSTA), making it more suitable for phased-array applications. With SODWI, we use a synthetic transmit element delay insertion (STEDI) approach which produces significant improvements in resolution, grating lobe level, and signal-to-noise ratio (SNR) over HMSTA. We also show how in SODWI a subset of the Hadamard codes can be sparsely selected to increase the imaging frame rate at the expense of image quality. SODWI is then compared with a variety of beamforming schemes for phased-array applications, including HMSTA, STEDI-HMSTA, diverging wave imaging (DWI), synthetic aperture (SA), and focused imaging. We present the results by implementing this technique on a 64-channel custom beamforming platform with a 40-MHz phased array. When a full set of codes is used, SODWI outperforms focused imaging contrast and SNR by 2.7 and 1.8 dB in addition to an 8× increase in frame rate, respectively.

Compressed sensing reconstruction of synthetic transmit aperture dataset for volumetric diverging wave imaging

A high volume rate and high performance ultrasound imaging method based on a matrix array is proposed by using compressed sensing (CS) to reconstruct the complete dataset of synthetic transmit aperture (STA) from three-dimensional (3D) diverging wave transmissions (i.e. 3D CS-STA). Hereto, a series of apodized 3D diverging waves are transmitted from a fixed virtual source, with the ith row of a Hadamard matrix taken as the apodization coefficients in the ith transmit event. Then CS is used to reconstruct the complete dataset, based on the linear relationship between the backscattered echoes and the complete dataset of 3D STA. Finally, standard STA beamforming is applied on the reconstructed complete dataset to obtain the volumetric image. Four layouts of element numbering for apodizations and transmit numbers of 16, 32 and 64 are investigated through computer simulations and phantom experiments. Furthermore, the proposed 3D CS-STA setups are compared with 3D single-line-transmit (SLT) and 3D diverging wave compounding (DWC). The results show that, (i) 3D CS-STA has competitive lateral resolutions to 3D STA, and their contrast ratios (CRs) and contrast-to-noise ratios (CNRs) approach to those of 3D STA as the number of transmit events increases in noise-free condition. (ii) the tested 3D CS-STA setups show good robustness in complete dataset reconstruction in the presence of different levels of noise. (iii) 3D CS-STA outperforms 3D SLT and 3D DWC. More specifically, the 3D CS-STA setup with 64 transmit events and the Random layout achieves ~31% improvement in lateral resolution, ~14% improvement in ratio of the estimated-to-true cystic areas, a higher volume rate, and competitive CR/CNR when compared with 3D DWC. The results demonstrate that 3D CS-STA has great potential of providing high quality volumetric image with a higher volume rate.