Beamforming Process Research Articles

Unlocking the Beamforming Potential of LoRa for Long-range Multi-target Respiration Sensing

Despite extensive research effort in contact-free sensing using RF signals in the last few years, there still exist significant barriers preventing their wide adoptions. One key issue is the inability to sense multiple targets due to the intrinsic nature of relying on reflection signals for sensing: the reflections from multiple targets get mixed at the receiver and it is extremely difficult to separate these signals to sense each individual. This problem becomes even more severe in long-range LoRa sensing because the sensing range is much larger compared to WiFi and acoustic based sensing. In this work, we address the challenging multi-target sensing issue, moving LoRa sensing one big step towards practical adoption. The key idea is to effectively utilize multiple antennas at the LoRa gateway to enable spatial beamforming to support multi-target sensing. While traditional beamforming methods adopted in WiFi and Radar systems rely on accurate channel information or transmitter-receiver synchronization, these requirements can not be satisfied in LoRa systems: the transmitter and receiver are not synchronized and no channel state information can be obtained from the cheap LoRa nodes. Another interesting observation is that while beamforming helps to increase signal strength, the phase/amplitude information which is critical for sensing can get corrupted during the beamforming process, eventually compromising the sensing capability. In this paper, we propose novel signal processing methods to address the issues above to enable long-range multi-target reparation sensing with LoRa. Extensive experiments show that our system can monitor the respiration rates of five human targets simultaneously at an average accuracy of 98.1%.

Flexible Electromagnetic Cap for Three-Dimensional Electromagnetic Head Imaging.

The timely treatment is the crucial element for the survival of patients with brain stroke. Thus, a fast, cost-effective, and portable device is needed for the early and on-the-spot diagnosis of stroke patients. A 3D electromagnetic head imaging system for rapid brain stroke diagnosis with a wearable and lightweight platform is presented. The platform comprises a custom-built flexible cap with a 24-element planar antenna array, and a flexible matching medium layer. The custom-built cap is made out of an engineered polymer-ceramic composite substrate of RTV silicone rubber and aluminum oxide (Al2O3) for enhanced dielectric properties and mechanical flexibility and robustness. The array is arranged into two elliptical rings that are entirely incorporated into the flexible cap. The employed antenna elements within the system are compact with low SAR values over the utilized frequency range of 0.9-2.5 GHz. Moreover, a flexible matching medium layer is introduced on the front of the apertures of the antenna array to enhance the impedance matching with the skin. The detection capability of the system is experimentally verified on 3D realistic head phantoms at multiple imaging scenarios and different types of strokes. The reconstructed 3D and 2D multi-slice images using the beamforming and polar sensitivity encoding (PSE) image processing algorithms indicate the applicability and potential of the system for onsite brain imaging.

Real-Time High Frame Rate Color Flow Mapping System.

Plane wave (PW) transmission (TX) can be profitably used to improve the performance of color flow mapping (CFM) systems by increasing the autocorrelation ensemble length (EL) and/or the frame rate (FR). Although high-end scanners tend to include imaging schemes using PW TX and parallel receive beams, high frame rate (HFR) CFM has been so far experimentally implemented mostly through research platforms that transmit PWs and beamform/process the received channel data off-line. In this article, full real-time implementation of PW CFM with continuous-time clutter filtering and extended FR/EL is reported. The field-programmable gate arrays (FPGAs) and digital signal processors (DSPs) onboard the ULA-OP 256 research scanner were programmed to perform high-speed parallel beamforming and autocorrelation-based CFM processing, respectively. Different strategies were tested, in which the TX of PWs for CFM is either continuous or interleaved with the TX of packets of B-mode pulses. A fourth-order Chebyshev continuous-time high-pass filter with programmable cutoff frequency was implemented and its clutter rejection performance was positively compared with that obtained when operating on packet data. CFM FRs up to 575 were obtained. The possibility of programming the autocorrelation EL up to 64 permitted to detect flow with high sensitivity and accuracy (average relative errors down to 0.4% ± 8.4%). In vivo HFR movies are presented, showing the dynamics of flow in the common carotid artery, which highlight the presence of secondary flow components.

Automatic slowness vector measurements of seismic arrivals with uncertainty estimates using bootstrap sampling, array methods and unsupervised learning

SUMMARYHorizontal slowness vector measurements using array techniques have been used to analyse many Earth phenomena from lower mantle heterogeneity to meteorological event location. While providing observations essential for studying much of the Earth, slowness vector analysis is limited by the necessary and subjective visual inspection of observations. Furthermore, it is challenging to determine the uncertainties caused by limitations of array processing such as array geometry, local structure, noise and their effect on slowness vector measurements. To address these issues, we present a method to automatically identify seismic arrivals and measure their slowness vector properties with uncertainty bounds. We do this by bootstrap sampling waveforms, therefore also creating random sub arrays, then use linear beamforming to measure the coherent power at a range of slowness vectors. For each bootstrap sample, we take the top N peaks from each power distribution as the slowness vectors of possible arrivals. The slowness vectors of all bootstrap samples are gathered and the clustering algorithm DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is used to identify arrivals as clusters of slowness vectors. The mean of slowness vectors in each cluster gives the slowness vector measurement for that arrival and the distribution of slowness vectors in each cluster gives the uncertainty estimate. We tuned the parameters of DBSCAN using a data set of 2489 SKS and SKKS observations at a range of frequency bands from 0.1 to 1 Hz. We then present examples at higher frequencies (0.5–2.0 Hz) than the tuning data set, identifying PKP precursors, and lower frequency by identifying multipathing in surface waves (0.04–0.06 Hz). While we use a linear beamforming process, this method can be implemented with any beamforming process such as cross correlation beamforming or phase weighted stacking. This method allows for much larger data sets to be analysed without visual inspection of data. Phenomena such as multipathing, reflections or scattering can be identified automatically in body or surface waves and their properties analysed with uncertainties.

Effects from correction of speed of sound in transmit and receive beamforming using focus beam

In this study, focusing methods were investigated for generation of an ultrasonic beam with a uniform lateral width across the axial imaging field of view through numerical simulation using Field II. Also, the influence of the mismatch between the speed of sound (SoS) assumed in beamforming process and actual one was evaluated by wire and cyst phantom experiments. In the simulation, conventional, hybrid, and non-cylindrical focusing methods were evaluated based on the evaluation metrics, i.e. depth of field and lateral beam width. For the three focusing methods, the proper imaging parameters were determined based on the simulation results. In the phantom experiments, the lateral resolution was improved by correcting the SoS in receive beamforming. Additionally, the correction of the SoS in transmission focusing improved the uniformity of beam width and image contrast.

A Fast Adaptive Beamforming Algorithm Based on Gram-Schmidt Orthogonalization

Fast implementation is one of the important indexes of the ADBF algorithm. The advantages of the Gram-Schmidt (GS) orthogonalization algorithm are that it can reconstruct the interference subspace well under the high signal-to-noise ratio and has fast convergence speed and low computational complexity. This paper studies the RGS algorithm for GS orthogonalization of sampling covariance matrix. To estimate the interference subspace more accurately, this paper modifies the orthogonal adaptive threshold of covariance matrix, and extends the proposed GS orthogonal algorithm of covariance matrix based on data preprocessing to the adaptive beamforming processing at subarray level.

Blockage-Aware Reliable mmWave Access via Coordinated Multi-Point Connectivity

The fundamental challenge of the millimeter-wave (mmWave) frequency band is the sensitivity of the radio channel to blockages, which gives rise to unstable connectivity and impacts the reliability of a system. To this end, multi-point connectivity is a promising approach for ensuring the desired rate and reliability requirements. A robust beamformer design is proposed to improve the communication reliability by exploiting the spatial macro-diversity and a pessimistic estimate of rates over potential link blockage combinations. Specifically, we provide a blockage-aware algorithm for the weighted sum-rate maximization (WSRM) problem with parallel beamformer processing across distributed remote radio units (RRUs). Combinations of non-convex and coupled constraints are handled via successive convex approximation (SCA) framework, which admits a closed-form solution for each SCA step, by solving a system of Karush-Kuhn-Tucker (KKT) optimality conditions. Unlike the conventional coordinated multi-point (CoMP) schemes, the proposed blockage-aware beamformer design has, per-iteration, computational complexity in the order of RRU antennas instead of system-wide joint transmit antennas. This leads to a practical and computationally efficient implementation that is scalable to any arbitrary multi-point configuration. In the presence of random blockages, the proposed schemes are shown to significantly outperform baseline scenarios and result in reliable mmWave communication.

The 2010 Haiti earthquake revisited: An acoustic intensity map from remote atmospheric infrasound observations

In the days following the January 12, 2010 Mw 7 Haiti earthquake the shaking intensity near the epicenter was overestimated and the spatial extent of the potentially damaging shaking was underestimated. This was due to the lack of seismometers in the near-source region at the time of the earthquake. Besides seismic waves, earthquakes generate infrasound, i.e., inaudible acoustic waves in the atmosphere. Here we show that infrasound signals, detected at distant ground-based stations, can be used to generate a map of the acoustic intensity, which is proportional to the shaking intensity. This is demonstrated with infrasound from the 2010 Haiti earthquake detected in Bermuda, over 1700 km away. Wavefront parameters are retrieved in a beamforming process and are backprojected to map the measured acoustic intensity to the source region. The backprojection process accounts for horizontal advection effects due to winds and inherent uncertainties with regard to the time of detection and the back azimuth resolution. Furthermore, we resolve the ground motion polarity in the epicentral region and use synthetics generated by an extended infrasound source model to support this result. Infrasound measurements are conducted globally for the verification of the Comprehensive Nuclear-Test-Ban Treaty and although the network was designed to provide global coverage for nuclear explosions in the atmosphere, it is shown in this paper that there is also global coverage for the estimation of acoustic shaking intensity. In this study, we lay the groundwork that can potentially make infrasound-based ShakeMaps a useful tool alongside conventional ShakeMaps and a valuable tool for earthquake disaster mitigation in sparsely monitored regions.

Optimization of Normalized Least Mean Square Algorithm of Smart Antenna Beamforming for Interference Mitigation

A smart antenna is an array of antennas with signal processing capabilities to transmit/receive information in an adaptive manner. This capability continues to be investigated to find the best adaptive algorithm for the desired beamforming capability. This paper aims to provide a study and analysis of the effect of the normalized least mean square (NLMS) algorithm on step size parameter settings which have an impact on the desired minimum square error (MSE) value and on the nulling beam radiation pattern arrangement of smart antennas in its role in mitigating interference. The simulation for beamformer performance for 1000 iterations was carried out using the Matlab tool on the additional white noise gaussian (AWGN) channel and the simulation parameters were changed to some step size values (μ) with the NLMS algorithm for 16 antenna elements. The effect of the value of the step size μ is seen in the iterations number that takes place before the minimum error noise is obtained, where the increase in the value of this step size reduces the iterations number required; at the same time further improving MSE levels. From the pattern of amplitude response after the beamforming process, the result is an escalation in the number of nulling to increase the distance between the spaced elements taken. The interference source is eliminated/closed by placing the nulls in the path of the interference source where the worst interference level is obtained around -90 dB when the smallest step size is taken.

Spatial‐Frequency Estimation for OFDM System with Coprime Array

Orthogonal frequency division multiplexing (OFDM) is the key technique of the communication system. In this paper, coprime array is designed in OFDM system to obtain joint direction of arrival (DOA) and carrier frequency offset (CFO) estimates. The proposed system can achieve beamforming and adaptive signal processing, reduce the multipath fading, and attain angle diversity. Meanwhile, coprime array has the advantages of extended array aperture, increased degrees of freedom, and reduced mutual coupling effect, which is adaptable in OFDM system. Moreover, this paper proposes a low‐complexity parameter algorithm with superior performance, which first exploits propagator method (PM) as the initialization and then parallel factor (PARAFAC) method is employed for the accurate DOA and CFO estimation. Simulation results verify the effectiveness of the OFDM coprime array system and the proposed low‐complexity multiparameter algorithm.

Robust Three-Microphone Speech Source Localization Using Randomized Singular Value Decomposition.

Direction-of-arrival (DOA) estimation is a fundamental technique in array signal processing due to its wide applications in beamforming, speech enhancement and many other assistive speech processing technologies. In this paper, we devise a novel DOA technique based on randomized singular value decomposition (RSVD) to improve the performance of non-uniform non-linear microphone arrays (NUNLA). The accurate and efficient singular value decomposition of large data matrices is computationally challenging, and randomization provides an effective tool for performing matrix approximation, therefore, the developed DOA estimation utilizes a modified dictionary-based RSVD method for localizing single speech sources under low signal-to-noise ratios (SNR). Unlike previous methods developed for uniform linear microphone arrays, the proposed approach with L-shaped three microphone setup has no ‘left-right’ ambiguity. We present the performance of our proposed method in comparison to other techniques. The demonstrated experiments shows at-least 20% performance improvement using simulated data and 25% performance improvement using real data when compared with similar DoA estimation techniques for NUNLA. The proposed method exploits frame-based online time delay of arrival (TDOA) measurements which facilitates the proposed algorithm to run on real-time devices. We also show an efficient real-time implementation of the proposed method on a Pixel 3 Android smartphone using its built-in three microphones for hearing aid applications.

Beamform processing for sonic imaging using monopole and dipole sources

New processing techniques are presented that enhance event signals for sonic imaging using monopole and dipole sources. The techniques use the azimuthally spaced receivers of a sonic logging tool. Sonic imaging, which is also known as borehole acoustic reflection surveys, uses a sonic logging tool in a fluid-filled borehole to image geologic structures. Signals from monopole and dipole sources are reflected from geologic interfaces and recorded by arrays of receivers of the same tool. Because the amplitudes of the event signals are very weak compared with the direct waves, borehole modes, and noise, the event signals are often difficult to extract. To enhance the weak event signals, beamforming techniques were developed to stack the waveforms from azimuthally spaced receivers of the tool for given azimuthal directions. For the incident P-waves from the monopole source, phase arrival times for the azimuthal receivers are time shifted for stacking using properties of wave propagation in the borehole. For the incident SH-waves from the dipole source, the signs of waveforms for the receivers are changed for specified azimuths. When the waveforms are stacked for the back azimuth of the event signals, the signal-to-noise ratio of the event signals is significantly improved because the event signals are enhanced whereas the direct waves are relatively smeared, and random noise is canceled. Therefore, the stacked waveforms also provide accurate back azimuths of the incident waves.

Modeling the temporal-spatial nature of the readout of an electronic portal imaging device (EPID).

In real-time electronic portal imaging device (EPID) dosimetry applications where on-treatment measured transmission images are compared to an ideal predicted image, ideally a tight tolerance should be set on the quantitative image comparison in order to detect a wide variety of possible delivery errors. However, this is currently not possible due to the appearance of banding artifacts in individual frames of the measured EPID image sequences. The purpose of this work was to investigate simulating banding artifacts in our cine-EPID predicted image sequences to improve matching of individual image frames to the acquired image sequence. Increased sensitivity of this method to potential treatment delivery errors would represent an improvement in patient safety and treatment accuracy. A circuit board was designed and built to capture the target current (TARG-I) and forward power signals produced by the linac to help model the discrete beam-formation process of the linac. To simulate the temporal-spatial nature of the EPID readout, a moving read out mask was applied with the timing of the application of the readout mask synchronized to the TARG-I pulses. Since identifying the timing of the first TARG-I pulse affected the location of the banding artifacts throughout the image sequence, and furthermore the first several TARG-I pulses at the beginning of "beam on" are not at full height yet (i.e., dose rate is ramping up), the forward-power signal was also used to assist in reliable detection of the first radiation pulse of the beam delivery. The predicted EPID cine-image sequence obtained using a comprehensive physics-based model was modified to incorporate the discrete nature of the EPID frame readout. This modified banding predicted EPID (MBP-EPID) image sequence was then compared to its corresponding measured EPID cine-image sequence on a frame-by-frame basis. The EPID was mounted on a Clinac 2100ix linac (Varian Medical Systems, Palo Alto, CA). The field size was set to 21.4 28.6cm2 with no MLC modulation, beam energy of 6MV, dose rate of 600MU/min, and 700MU were delivered for each clockwise (CW) and counter-clockwise (CCW) arc. No phantoms were placed in the beam. The dose rate ramp up effect was observed at the beginning irradiations, and the identification and timing of the radiation pulses, even during the dose rate ramp up, were able to be quantified using the TARG-I and forward power signals. The approach of capturing individual dose pulses and synchronizing with the mask image applied to the original predicted EPID image sequence was demonstrated to model the actual EPID readout. The MBP-EPID image sequences closely reproduced the location and magnitude of the banding features observed in the acquired (i.e., measured) image sequence, for all test irradiations examined here. The banding artifacts observed in the measured EPID cine-frame sequences were reproduced in the predicted EPID cine-frames by simulating the discrete temporal-spatial nature of the EPID read out. The MBP-EPID images showed good agreement qualitatively to the corresponding measured EPID frame sequence of a simple square test field, without any phantom in the beam. This approach will lead to improved image comparison tolerances for real-time patient dosimetry applications.

A Minimum-Energy-Based Algorithm for Multichannel Reconstruction

For the azimuth multichannel synthetic aperture radar (SAR), nonuniform sampling is common since the pulse-repetition frequency cannot be selected arbitrarily, which leads to the contradiction between ambiguity and noise suppression in the azimuth signal reconstruction. This letter constructs a novel multichannel signal model by taking the coherence among different Doppler bins into account and proposes a minimum-energy-based multichannel reconstruction algorithm, which can obtain the unambiguous signal spectrum without increasing noise in the nonuniform sampling cases. By comparing the simulation results formed by digital beamforming (DBF), improved DBF (IDBF), and space-time adaptive processing (STAP) algorithms, the proposed algorithm shows better performance in balancing ambiguity and noise.

Analysis of the Time and Phase Delay Resolutions in Ultrasound Baseband I/Q Beamformers.

The ultrasound baseband in-phase/quadrature beamformer (IQBF) has been widely employed in medical ultrasound imaging to reduce the amount of channel data or to decrease the data rate of the beamforming process. The aim of this study is to assess the effect of the time and phase delay compensation accuracies on the IQBF and thereby to suggest the criteria for selecting the delay resolutions of the IQBF. Mathematical models of the gain loss (GL) and sidelobe level (SL) in closed form are suggested, and the relationships between the parameters (time and phase delay resolutions of the IQBF and the signal bandwidth) and the errors (GL and SL) are investigated. The performance of the IQBF is compared with that of the traditional radio-frequency beamformer (RFBF). Simulation and phantom and in vivo experimental results are shown to corroborate the theoretical analysis. Theoretical analysis and simulation and experimental results show that a phase delay resolution with a quantization step of 2π/64 is sufficient for phase compensation and that a time delay resolution with a sampling rate of 4f0 and 2f0 in the IQBF is sufficient for data with a -6 dB bandwidth of 50% and 25%, respectively, for similar performance as the RFBF with a sampling rate of 16f0, where f0 is the center frequency of the ultrasound signal. The suggested criteria have the potential to be used for designing an efficient IQBF satisfying the desired specifications and beamforming accuracy.

An Orthogonal Hybrid Analog–Digital Multibeam Antenna Array for Millimeter-Wave Massive MIMO Systems

A hybrid analog-digital multibeam antenna array (MBAA) consisting of two types of 1-D beamformers for two orthogonal planes, respectively, is proposed for massive multiple-input multiple-output (MIMO) communication systems at millimeter-waves. In the vertical direction, the multiple beams are generated by a passive beamformer, i.e., a Butler matrix, whereas the multibeam coverage in the horizontal plane is achieved digitally at the baseband. Comparing to a full-digital multibeam array, the digital beamforming (DBF) processing is simplified in the proposed scheme, significantly alleviating the computational burden of data processing. Since the radiation beams are generated by only a part of the radio frequency (RF) channels in the hybrid multibeam array, the power consumption could be reduced by powering down the idle channels. To verify the concept, a two-dimensional (2-D) array comprised by 16 columns of eight-beam tapered slot antenna subarrays is designed and fabricated, in which each subarray contains a pair of 4 × 8 modified Butler matrices based on the substrate-integrated waveguide technology. The measured results exhibit that the operating bandwidth is 13.45% for the subarray fed by the modified Butler matrices implemented by substrate-integrated waveguides. The RF receivers, intermediate frequency (IF) chains, and analog-to-digital converters (ADCs) are also implemented to enable the DBF in the horizontal plane. The maximum simulated directivity of the array is 27 dBi. A wide 2-D spatial angle is covered simultaneously by the proposed hybrid passive-DBF scheme. The demonstrated 2-D millimeter-wave hybrid array may find widespread potential applications in future communication systems.

Photoacoustic imaging for surgical guidance: Principles, applications, and outlook.

Minimally invasive surgeries often require complicated maneuvers and delicate hand–eye coordination and ideally would incorporate “x-ray vision” to see beyond tool tips and underneath tissues prior to making incisions. Photoacoustic imaging has the potential to offer this feature but not with ionizing x-rays. Instead, optical fibers and acoustic receivers enable photoacoustic sensing of major structures—such as blood vessels and nerves—that are otherwise hidden from view. This imaging process is initiated by transmitting laser pulses that illuminate regions of interest, causing thermal expansion and the generation of sound waves that are detectable with conventional ultrasound transducers. The recorded signals are then converted to images through the beamforming process. Photoacoustic imaging may be implemented to both target and avoid blood-rich surgical contents (and in some cases simultaneously or independently visualize optical fiber tips or metallic surgical tool tips) in order to prevent accidental injury and assist device operators during minimally invasive surgeries and interventional procedures. Novel light delivery systems, counterintuitive findings, and robotic integration methods introduced by the Photoacoustic & Ultrasonic Systems Engineering Lab are summarized in this invited Perspective, setting the foundation and rationale for the subsequent discussion of the author’s views on possible future directions for this exciting frontier known as photoacoustic-guided surgery.

On the Polarimetric Variable Improvement via Alignment of Subarray Channels in PPAR Using Weather Returns

Many modern phased-array radars (PARs) are multichannel systems that include multiple receivers for data acquisition. Each channel provides a signal from a group of Transmit/Receive modules comprising a section of the antenna. Channels typically consist of a full receive path, often with an independent local oscillator (LO) clock source. Such arrangement provides for beamforming flexibility on receive which can be applied in a digital domain. Consequently, the channel-to-channel phase and magnitude alignment is critical to maximizing the performance of the digital beamforming process and the accuracy of resulting detections and measurements. Herein, a novel method to improve such alignment using weather returns and achieve the improvement in the polarimetric variable estimates is described.

Spatiotemporal Dielectric Metasurfaces for Unidirectional Propagation and Reconfigurable Steering of Terahertz Beams.

Next-generation devices for low-latency and seamless communication are envisioned to revolutionize information processing, which would directly impact human lives, technologies, and societies. The ever-increasing demand for wireless data traffic can be fulfilled by the terahertz band, which has received tremendous attention as the final frontier of the radio spectrum. However, attenuation due to atmospheric humidity and free-space path loss significantly limits terahertz signal propagation. High-gain antennas with directional radiation and reconfigurable beam steering are indispensable for loss compensation and terahertz signal processing, which are associated with spatial and temporal dimensions, respectively. Here, experimental demonstration of a spatiotemporal dielectric metasurface for unidirectional propagation and ultrafast spatial beam steering of terahertz waves is shown. The spatial dimension of the metasurface provides a solution to eliminate backscattering of collimated unidirectional propagation of the terahertz wave with steerable directionality. Temporal modulation of the spatial optical properties enables ultrafast reconfigurable beam steering. Silicon-based spatiotemporal devices amalgamate the rich physics of metasurfaces and technologies that are promising for overcoming the bottlenecks of future terahertz communication, such as high-speed and secure wireless data transmission, beamforming and ultrafast data processing.

A fast and high frame rate adaptive beamforming using DCT‐based RF‐line recovery in line‐by‐line ultrasound imaging

AbstractUltrasound imaging is an important modality used in medical imaging. One of the significant stages in the ultrasound imaging is the beamforming process. This article proposes a new technique for reducing the overall computational time of adaptive linear ultrasound imaging. The method uses the discrete cosine transform‐based reconstruction for missing data imputation. The novelty of the paper is that we do not need to beam‐form the total scan lines, so the time of image construction can be saved significantly. In other words, a fraction of the total scan lines is selected for beamforming and the others are assumed to have values as Not‐a‐Number (NaN). The proposed reconstruction technique tries to assign appropriate values to the NaN ones. We applied the proposed method to the simulated and experimental radio frequency (RF) datasets for resolution and contrast evaluation. Results showed that the proposed technique is near to the minimum variance (MV) method in terms of resolution and contrast, and has less computational time for image formation compared to the MV. As some quantitative examples in some experiments we have formed only 50% and 33% of the total lines and reconstructed the rest, then we have been able to increase the frame rate twice and three times, respectively, which can be very useful in many applications, especially in echocardiography imaging. In addition, since the execution time of the reconstruction algorithm is not very significant, we were also able to increase the speed by two and three times while achieving an error of less than 10% compared to the case of using all image lines.