Compressed Sensing Based Synthetic Transmit Aperture Imaging: Validation in a Convex Array Configuration

Enhancing single-element compressive ultrasound imaging through novel random aperture masking and data mixing strategy

As ultrasound techniques continue to evolve, the integration of compressed sensing technology has emerged as a pivotal advancement, offering a transformative impact on the landscape of ultrasound imaging. A key attribute of compressed sensing lies in its ability to facilitate a substantial reduction in both machinery size and power consumption. This technological synergy not only addresses crucial practical considerations in the design of ultrasound systems but also opens avenues for enhanced portability and energy efficiency. This study develops a model and introduces an aperture mask with a mixing scheme for compressive ultrasound imaging employing a single transducer, aiming to minimize the loss of information and scrutinize the variables influencing image quality while facilitating computationally efficient system simulation. A detailed procedural guide is presented for generating synthetic data, accompanied by qualitative and quantitative analyses using several sparse recovery methods under different experimental conditions. This study's analysis reveals that the proposed strategy achieves improved metrics, offering advantages for sparse recovery. Specifically, the finite element results demonstrate approximately a 10% improvement in the condition number of the measurement matrix, reflecting enhanced numerical stability.

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.

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.

Temporal Super-resolution of Ultrasound Imaging Using Matrix Completion

The temporal super-resolution of the dynamic ultrasound imaging, a means to observe rapid heart movements, is considered an important subject in medical diagnosis of cardiac conditions. Here, a new technique based on the acquisition scheme using the matrix completion (MC) theory is offered for the temporal super-resolution of the two-dimensional (2D) and three-dimensional (3D) ultrasound imaging. MC mentions the problem of completing a low-rank matrix when only a subset of its elements can be observed. Here, the lower scan lines are acquired. Whereby, the proposed method uses temporal and spatial information of the radio frequency (RF) image sequences for the reconstruction of skipped RF lines. This is performed using the construction of the MC images and then reconstruction of them by the MC theory. The results of the proposed method are compared with the compressive sensing (CS) reconstruction methods. The qualitative and quantitative evaluations of 2D and 3D data demonstrate that in the proposed method, which uses the spatial and temporal relation of RF images and the MC theory, the reconstruction is more accurate, and the reconstruction error is lower. The computational complexity of this method is very low. It also does not require hardware adjustments. Therefore, it can be easily implemented in current ultrasound-imaging devices with the frame-rate enhancement. For instance, the frame rate up to two times the original sequence is feasible using the proposed methods, while root mean square error is decreased by about 35% and 30% for 2D and 3D data, respectively, compared with the CS reconstruction method.

Adaptive block forward and backward stagewise orthogonal matching pursuit algorithm applied to rolling bearing fault signal reconstruction

In the process of block compressed sensing (CS) applied to the rolling bearing fault signal, the reconstruction accuracy of the signal is low due to the large difference in sparsity between blocks and the unreasonable components of reconstruction support set, which affects the overall reconstruction effect of the signal. To improve the signal reconstruction results, forward and backward stagewise orthogonal matching pursuit (FBStOMP) based on the adaptive block method is proposed. First, to equalize the sparsity of each block signal, the fault signal is divided into blocks according to the adaptive block length, which is obtained by the short-time autocorrelation algorithm. Then, the K-singular value decomposition algorithm is used to train the sparse dictionary to obtain a better sparse effect. Finally, the FBStOMP algorithm is proposed. The atom backtracking and screening process is added in the reconstruction process to improve the possibility that all the effective atoms can be selected into the support set. The experimental analysis of the simulation signal and bearing fault signal show that, compared with the traditional CS reconstruction algorithm, the adaptive block-FBStOMP algorithm proposed in the paper can effectively improve the reconstruction accuracy of the bearing fault signal.

Compressed Ultrasound Signal Reconstruction Using a Low-Rank and Joint-Sparse Representation Model

With the introduction of very dense sensor arrays in ultrasound (US) imaging, data transfer rate and data storage can become a bottleneck in US system design. To reduce the amount of sampled channel data, we propose a new approach based on the low-rank and joint-sparse model that allows us to exploit the correlations between different US channels and transmissions. With this method, the minimum number of measurements at each channel can be lower than the sparsity in compressive sensing theory. The accuracy of the reconstruction is less dependent on the sparse basis. An optimization algorithm based on the simultaneous direction method of multipliers is proposed to efficiently solve the resulting optimization problem. Results on different data sets with different experimental settings show that the proposed method is better adapted to the US signals and can recover the image with fewer samples (e.g., 10% of the samples) than the existing compressive sensing-based methods, while maintaining reasonable image quality.

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.

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

Previously, we proposed compressed sensing based synthetic transmit aperture (CS-STA) to improve the contrast and frame rate of STA while maintaining its spatial resolution in linear array by choosing uniform random matrix as the measurement matrix and transmitting the plane waves (PWs). In this paper, to extend CS-STA for phased array imaging and further improve its performance, we design four types of CS-STA implementations with different combinations of measurement matrices (i.e., uniform random and Hadamard matrices) and transmitted waves [i.e., PW and diverging wave (DW)]. Through simulations and phantom experiments with a 3 MHz, 64-element phased array, we find that type-IV CS-STA with the combination of a Hadamard matrix and DW outperforms the other three implementations including the previously proposed type-I CS-STA in terms of image quality and reconstruction time. Specifically, PW transmission produces visible discontinuity and the reconstruction time with uniform random matrix is about 100-fold longer than that with the Hadamard matrix. Compared with STA, with eightfold higher frame rate, type-IV CS-STA achieves 8.2 and 12.3 dB higher contrast-to-noise ratio and signal-to-noise ratio in the simulations, respectively. These improvements are slightly lower in the phantom experiments, which are 6.2 and 6.6 dB, respectively. In addition, CS-STA does not deteriorate the spatial resolution of STA, with the maximum deterioration being smaller than 1/8 wavelength. These results demonstrate that type-IV CS-STA can achieve phased array imaging with high image quality at high frame rate and may be beneficial to cardiac imaging.