The standard technique used by commercial medical ultrasound systems to form B-mode images is delay and sum (DAS) beamforming. However, DAS often results in limited image resolution and contrast, which are governed by the center frequency and the aperture size of the ultrasound transducer. A large number of elements leads to improved resolution but at the same time increases the data size and the system cost due to the receive electronics required for each element. Therefore, reducing the number of receiving channels while producing high quality images is of great importance. In this paper, we introduce a nonlinear beamformer called COnvolutional Beamforming Algorithm (COBA), which achieves significant improvement of lateral resolution and contrast. In addition, it can be implemented efficiently using the fast Fourier transform. Based on the COBA concept, we next present two sparse beamformers with closed form expressions for the sensor locations, which result in the same beam pattern as DAS and COBA while using far fewer array elements. Optimization of the number of elements shows that they require a minimal number of elements which is on the order of the square root of the number used by DAS. The performance of the proposed methods is tested and validated using simulated data, phantom scans and in vivo cardiac data. The results demonstrate that COBA outperforms DAS in terms of resolution and contrast and that the suggested beamformers offer a sizable element reduction while generating images with an equivalent or improved quality in comparison to DAS.
Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data affects both machinery size and power consumption. Within the classical sampling framework, state of the art systems reduce processing rates by exploiting the bandpass bandwidth of the detected signals. It has been recently shown, that a much more significant sample-rate reduction may be obtained, by treating ultrasound signals within the Finite Rate of Innovation framework. These ideas follow the spirit of Xampling, which combines classic methods from sampling theory with recent developments in Compressed Sensing. Applying such low-rate sampling schemes to individual transducer elements, which detect energy reflected from biological tissues, is limited by the noisy nature of the signals. This often results in erroneous parameter extraction, bringing forward the need to enhance the SNR of the low-rate samples. In our work, we achieve SNR enhancement, by beamforming the sub-Nyquist samples obtained from multiple elements. We refer to this process as “compressed beamforming”. Applying it to cardiac ultrasound data, we successfully image macroscopic perturbations, while achieving a nearly eightfold reduction in sample-rate, compared to standard techniques. Covering the fundamental mathematical underpinnings together with key principles and applications, this book provides a comprehensive guide to the theory and practice of sampling from an engineering perspective. Beginning with traditional ideas such as uniform sampling in shift-invariant spaces and working through to the more recent fields of compressed sensing and sub-Nyquist sampling, the key concepts are addressed in a unified and coherent way. Emphasis is given to applications in signal processing and communications, as well as hardware considerations, throughout. With 200 worked examples and over 200 end-of-chapter problems, this is an ideal course textbook for senior undergraduate and graduate students. It is also an invaluable reference or self-study guide for engineers and students across industry and academia. A novel beamforming technique, named compressed sensing based synthetic transmit aperture (CS-STA) is proposed to speed up the acquisition of ultrasound imaging. This technique consists of three steps. First, the ultrasound transducer transmits randomly apodized plane waves for a number of times and receives the backscattered echoes. Second, the recorded backscattered echoes are used to recover the full channel dataset of synthetic transmit aperture (STA) with a compressed sensing (CS) reconstruction algorithm. Finally, an STA image is beamformed from the recovered full STA dataset. As CS allows recovering a signal from its few linear measurements with high probability, CS-STA is capable of recovering the STA image with fewer firings (i.e., higher frame rate) and retaining the high resolution of STA. In addition, the contrast of the STA image can be improved at the same time owing to the higher energy of plane wave firing in CS-STA. Simulations demonstrate that CS-STA is capable of recovering the STA channel dataset with a smaller number of firings. The performance of CS-STA is evaluated in phantom experiments through comparisons with STA, multi-element STA, conventional focused mode and coherent plane wave imaging. The results demonstrate that, implemented with the same frame rate, CS-STA achieves higher or comparable resolution and contrast. Moreover, comparisons are conducted on the biceps brachii muscle and thyroid of a human subject, and the results demonstrate the feasibility and competitiveness of CS-STA in the in vivo conditions. Ultrafast imaging based on coherent plane-wave compounding is one of the most important recent developments in medical ultrasound. It significantly improves the image quality and allows for much faster image acquisition. This technique, however, requires large computational load motivating methods for sampling and processing rate reduction. In this work, we extend the recently proposed frequency-domain beamforming (FDBF) framework to plane-wave imaging. Beamforming in frequency yields the same image quality while using fewer samples. It achieves at least fourfold sampling and processing rate reduction by avoiding oversampling required by standard processing. To further reduce the rate, we exploit the structure of the beamformed signal and use compressed sensing methods to recover the beamformed signal from its partial frequency data obtained at a sub-Nyquist rate. Our approach obtains tenfold rate reduction compared with standard time-domain processing. We verify performance in terms of spatial resolution and contrast based on the scans of a tissue mimicking the phantom obtained by a commercial Aixplorer system. In addition, in vivo carotid and thyroid scans processed using standard beamforming and FDBF are presented for qualitative evaluation and visual comparison. Finally, we demonstrate the use of FDBF for shear-wave elastography by generating velocity maps from the beamformed data processed at sub-Nyquist rates. Abstract Compressive sensing (CS) theory makes it possible – under certain assumptions – to recover a signal or an image sampled below the Nyquist sampling limit. In medical ultrasound imaging, CS could allow lowering the amount of acquired data needed to reconstruct the echographic image. CS thus offers the perspective of speeding up echographic acquisitions and could have many applications, e.g. triplex acquisitions for CFM B-mode Doppler imaging, high-frame-rate echocardiography, 3D imaging using matrix probes, etc. The objective of this paper is to study the feasibility of CS for the reconstruction of channel RF data, i.e. the 2D set of raw RF lines gathered at the receive elements. Successful application of CS implies selecting a representation basis where the data to be reconstructed have a sparse expansion. Because they consist mainly in warped oscillatory patterns, channel RF data do not easily lend themselves to a sparse representation and thus represent a specific challenge. Within this perspective, we propose to perform and assess CS reconstruction of channel RF data using the recently introduced wave atoms [1] representation, which exhibit advantageous properties for sparsely representing such oscillatory patterns. Reconstructions obtained using wave atoms are compared with the reconstruction performed with two conventional representation bases, namely Fourier and Daubechies wavelets. The first experiment was conducted on simulated channel RF data acquired from a numerical cyst phantom. The quality of the reconstructions was quantified through the mean absolute error at varying subsampling rates by removing 50–90 of the original samples. The results obtained for channel RF data reconstruction yield error ranges of [0.6–3.0] × 10−2, [0.2–2.6] × 10−2, [0.1–1.5] × 10−2, for wavelets, Fourier and wave atoms respectively. The error ranges observed for the associated beamformed log-envelope images are [2.4–20.6] dB, [1.1–12.2] dB, and [0.5–8.8 dB] using wavelets, Fourier, and wave atoms, respectively. These results thus show the superiority of the wave atom representation and the feasibility of CS for the reconstruction of US RF data. The second experiment aimed at showing the experimental feasibility of the method proposed using a data set acquired by imaging a general-purpose phantom (CIRS Model 054GS) using an Ultrasonix MDP scanner. The reconstruction was performed by removing 80 of the initial samples and using wave atoms. The reconstructed image was found to reliably preserve the speckle structure and was associated with an error of 5.5 dB. Sonography techniques use multiple transducer elements for tissue visualization. Signals received at each element are sampled before digital beamforming. The sampling rates required to perform high-resolution digital beamforming are significantly higher than the Nyquist rate of the signal and result in considerable amount of data that must be stored and processed. A recently developed technique, compressed beamforming, based on the finite rate of innovation model, compressed sensing (CS), and Xampling ideas, allows a reduction in the number of samples needed to reconstruct an image comprised of strong reflectors. A drawback of this method is its inability to treat speckle, which is of significant importance in medical imaging. Here, we build on previous work and extend it to a general concept of beamforming in frequency. This allows exploitation of the low bandwidth of the ultrasound signal and bypassing of the oversampling dictated by digital implementation of beamforming in time. By using beamforming in frequency, the same image quality is obtained from far fewer samples. We next present a CS technique that allows for further rate reduction, using only a portion of the beamformed signal's bandwidth. We demonstrate our methods on in vivo cardiac data and show that reductions up to 1 28 of the standard beamforming rates are possible. Finally, we present an implementation on an ultrasound machine using sub-Nyquist sampling and processing. Our results prove that the concept of sub-Nyquist processing is feasible for medical ultrasound, leading to the potential of considerable reduction in future ultrasound machines' size, power consumption, and cost. Machine generated contents note: 1. Introduction to compressed sensing Mark A. Davenport, Marco F. Duarte, Yonina C. Eldar and Gitta Kutyniok; 2. Second generation sparse modeling: structured and collaborative signal analysis Alexey Castrodad, Ignacio Ramirez, Guillermo Sapiro, Pablo Sprechmann and Guoshen Yu; 3. Xampling: compressed sensing of analog signals Moshe Mishali and Yonina C. Eldar; 4. Sampling at the rate of innovation: theory and applications Jose Antonia Uriguen, Yonina C. Eldar, Pier Luigi Dragotta and Zvika Ben-Haim; 5. Introduction to the non-asymptotic analysis of random matrices Roman Vershynin; 6. Adaptive sensing for sparse recovery Jarvis Haupt and Robert Nowak; 7. Fundamental thresholds in compressed sensing: a high-dimensional geometry approach Weiyu Xu and Babak Hassibi; 8. Greedy algorithms for compressed sensing Thomas Blumensath, Michael E. Davies and Gabriel Rilling; 9. Graphical models concepts in compressed sensing Andrea Montanari; 10. Finding needles in compressed haystacks Robert Calderbank, Sina Jafarpour and Jeremy Kent; 11. Data separation by sparse representations Gitta Kutyniok; 12. Face recognition by sparse representation Arvind Ganesh, Andrew Wagner, Zihan Zhou, Allen Y. Yang, Yi Ma and John Wright.