Minimum Variance Approaches to Ultrasound Pixel-Based Beamforming

Vessel recovery using ultrasound localisation microscopy: An in silico comparative study between minimum variance and delay-and-sum beamformers

The use of particle localisation and tracking algorithms on Contrast Enhanced Ultrasound (CEUS) or other ultrasound mode image data containing sparse microbubble (MB) populations, can produce super-resolved vascularization maps. Typically such data stem from conventional delay and sum (DAS) beamforming that is used widely in ultrasound imaging modes. Recently, adaptive beamforming has shown significant improvement in spatial resolution, but its value to super-resolution image analysis approaches is not fully understood. The in silico study here evaluates the performance of combining minimum variance beamformers (MV BF), established to provide improved lateral resolution, compared to DAS BFs with single particle detection. The isolated effect of a range of simplified image-affecting factors such as flow profile, pulse length, noise, vessel separations and data availability is considered. The study aims to assess the vessel recovery performance using the different beamformers and investigate the link with MB detection and localisation. The MV BF was shown to provide improved microvessel position accuracy compared to conventional DAS BFs. In particular, vessel separations between 0.3-4 λ provided superior localisation uncertainty with the MV. In addition, for a separation of 0.36λ, vessel recovery was achieved with both methods but the use of MV eliminated artifacts that appear as additional vessels. These results were found to be linked to improved MB detection and localisation for the MV BF, which is proposed as suitable for testing in Ultrasound Localisation Microscopy (ULM) imaging using patient data.

Real-time passive cavitation mapping and B-mode fusion imaging via hybrid adaptive beamformer with modified diagnostic ultrasound platform

The implementation of real-time, convenient and high-resolution passive cavitation imaging (PCM) is crucial for ensuring the safety and effectiveness of ultrasound applications related to cavitation effects. However, the current B-mode ultrasound imaging system cannot achieve these functions. By developing a hybrid adaptive beamforming algorithm, the current work presented a real-time PCM and B-mode fusion imaging technique, using a modified diagnostic ultrasound platform enabling time-division multiplexing external triggering function. The proposed hybrid adaptive beamformer combined the advantages of delay-multiply-and-sum (DMAS) and minimum variance (MV) methods to effectively suppress the side lobe and tail-like artifacts, improving the resolution of PCM images. A high-pass filter was applied to selectively detect cavitation-specific signals while removing the interference from the tissue scatters. The system enabled synchronous visualization of tissue structure and cavitation activity under ultrasound exposure. Both numerical and experimental studies demonstrated that, compared with DAS, MV-DAS and DMAS methods, the proposed MV-DMAS algorithm performed better in both axial and lateral resolutions. This work represented a significant advancement in achieving high-quality real-time B-mode and PCM fusion imaging utilizing commercial medical ultrasound system, providing a powerful tool for synchronous monitoring and manipulating cavitation activity, which would enhance the safety and efficacy of cavitation-based applications.

On the physics of ultrasound transmission for in-plane needle tracking in guided interventions

Objective.In ultrasound (US) guided interventions, the accurate visualization and tracking of needles is a critical challenge, particularly during in-plane insertions. An inaccurate identification and localization of needles lead to severe inadvertent complications and increased procedure times. This is due to the inherent specular reflections from the needle with directivity depending on the angle of incidence of the US beam, and the needle inclination.Approach.Though several methods have been proposed for improved needle visualization, a detailed study emphasizing the physics of specular reflections resulting from the interaction of transmitted US beam with the needle remains to be explored. In this work, we discuss the properties of specular reflections from planar and spherical wave US transmissions respectively through multi-angle plane wave (PW) and synthetic transmit aperture (STA) techniques for in-plane needle insertion angles between 15°-50°.Main Results.The qualitative and quantitative results from simulations and experiments reveal that the spherical waves enable better visualization and characterization of needles than planar wavefronts. The needle visibility in PW transmissions is severely degraded by the receive aperture weighting during image reconstruction than STA due to greater deviation in reflection directivity. It is also observed that the spherical wave characteristics starts to alter to planar characteristics due to wave divergence at large needle insertion depths.Significance.The study highlights that synergistic transmit-receive imaging schemes addressing the physical properties of reflections from the transmit wavefronts are imperative for the precise imaging of needle interfaces and hence have strong potential in elevating the quality of outcomes from US guided interventional practices.

An adaptive beamformer based on dynamic phase coherence factor for pixel-based medical ultrasound imaging

BACKGROUND

Pixel-based beamforming realizes dynamic focusing at the pixel level with a focused beam by assuming that the received signals are composed of spherical pulses. Far-focused pixel-based (FPB) imaging was proposed to avoid artifacts around the focal depth. However, the contrast improvement is limited.

OBJECTIVE

We propose an adaptive weighting method based on dynamic phase coherence factor (DPCF) to improve the image contrast while preserving the speckle pattern.

METHODS

The phase variation is dynamically estimated based on the noise energy proportion of echo signals and it is used to calculate phase coherence weights for suppressing interference and preserving desired signals. A depth-dependent parameter is designed for DPCF to enhance the performance of noise and clutter suppression in the far-field region. We further use the subarray averaging technique to smooth the speckle texture.

RESULTS

The proposed method was evaluated on simulated, phantom experimental, and in vivo data. Results show that, compared with the phase coherence factor (PCF) based method, DPCF respectively leads to average CR improvements by more than 60% and 24% in simulation and experiment, while obtaining an improved speckle signal-to-noise ratio.

CONCLUSIONS

The proposed method is a potentially valuable approach to obtaining high-quality ultrasound images in clinical applications.

Improvising limitations of DNN based ultrasound image reconstruction

Ultrasound modalities are cost-effective and radiation-free technology for real-time medical imaging. These modalities require image reconstruction to obtain the actual ultrasound images from ultrasound raw data. The ultrasound raw data is obtained in the form of echo after scanning an imaging plane through ultrasound waves. The most commonly used image reconstruction beamforming technique is Delay and Sum (DAS). Other sophisticated beamforming techniques are Delay Multiply and Sum (DMAS) and Minimum Variance Distortionless Response (MVDR). DAS has limited image quality, and the employment of sophisticated techniques increases the computational complexity and computational time with improvement in image quality. To overcome these problems, various DNN (Deep Neural Networks) based techniques have been proposed which can reconstruct ultrasound images directly from ultrasound raw data. But DNN implementation has two limitations: accuracy of reconstruction and generalizability of the model. To overcome these limitations, we are proposing methodologies with a DNN model which was able to reduce these limitations. Firstly, we generated the datasets which include multiple shapes such as line, circle, ellipse, and parabola. After that, we have implemented a CNN-DNN (Convolution Neural Network and Deep Neural Network) hybrid model which has significantly improved computational time as well as image quality. We have trained our model with different sets of data to validate the reconstruction of the image matrix. We achieved a significant improvement in computational time of around 100 times (from around 0.6 s to 0.0059 s) as compared to DAS beamforming technique. At the same time, we also achieved a significant improvement in image quality with 37.19 dB average and 41.37 dB maximum improved Peak Signal to Noise Ratio (PSNR), and 87.41% average and 95% maximum Structural Similarity Index Matrix (SSIM) value. We also achieved generalizability and precise image reconstruction by using the proposed model.

Towards Fast Region Adaptive Ultrasound Beamformer for Plane Wave Imaging Using Convolutional Neural Networks

Automatic learning algorithms for improving the image quality of diagnostic B-mode ultrasound (US) images have been gaining popularity in the recent past. In this work, a novel convolutional neural network (CNN) is trained using time of flight corrected in-vivo receiver data of plane wave transmit to produce corresponding high-quality minimum variance distortion less response (MVDR) beamformed image. A comprehensive performance comparison in terms of qualitative and quantitative measures for fully connected neural network (FCNN), the proposed CNN architecture, MVDR and Delay and Sum (DAS) using the dataset from Plane wave Imaging Challenge in Ultrasound (PICMUS) is also reported in this work. The CNN architecture can leverage the spatial information and will be more region adaptive during the beamforming process. This is evident from the improvement seen over the baseline FCNN approach and conventional MVDR beamformer, both in resolution and contrast with an improvement of 6 dB in CNR using only zero-angle transmission over the baseline. The observed reduction in the requirement of number of angles to produce similar image metrics can provide a possibility for higher frame rates.

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.

Ultrasound far-focused pixel-based imaging using Wiener postfilter scaled by adjustable zero-cross factor

Synthetic aperture (SA) imaging can provide a uniform lateral resolution but an insufficient signal-to-noise ratio (SNR). SA method with bidirectional pixel-based focusing (SA-BiPBF) has the ability to obtain a higher quality image than conventional SA imaging. In this paper, an enhanced SA-BiPBF named full aperture received far-focused pixel-based (FrFPB) is firstly proposed to obtain a high resolution image. An adjustable zero-cross factor scaled Wiener postfilter (AZFsW) is then implemented in FrFPB for improving contrast ratio (CR). The adjustable zero-cross factor is calculated using the polarity of echo signals sequence with an adjustable coefficient σ to estimate the signal coherence, and it is combined with Wiener postfilter to obtain a good capability of noise reduction and background speckle pattern preservation. Simulation and experiments have been conducted to evaluate the imaging performance of the proposed methods. Results show that FrFPB can obviously improve the resolution in comparison with SA-BiPBF, and contrast-to-noise ratio (CNR) and speckle signal-to-noise ratio (sSNR) are retained. In addition, AZFsW can achieve a much higher CR than SA-BiPBF. When σ is 0.6, the CR improvement is 96.7% in simulation, 78.7% in phantom experiment, and 49.2% in in-vivo experiment. To evaluate the imaging performance of AZFsW, coherence factor, conventional Wiener postfilter, and scaled Wiener postfilter are implemented. The imaging results show that when σ is in the range of [0.6, 0.7], AZFsW exhibits a satisfying comprehensive imaging performance.

User Parameter-Free Minimum Variance Beamformer in Medical Ultrasound Imaging

The minimum variance beamformer (MVB) is a well-known adaptive beamformer in medical ultrasound imaging. Accurate estimation of the covariance matrix has a great effect on the performance of the MVB. In adaptive ultrasound imaging, parameters such as the subarray length, the number of samples used for temporal averaging, and the value of diagonal loading (DL) have the main role in the true estimation of the covariance matrix. The optimal values for these parameters are different from one scenario to another one. Thus, the MVB is not a parameter-free method, and its behavior is scenario-dependent. In the field of telecommunications and radar, the shrinkage method was proposed to determine the DL factor, but no method has been provided yet to determine other parameters. In this article, an adaptive approach is developed to determine the MVB parameters, which is completely independent of the user. The minimum variance variable loading along with the modified shrinkage (MVVL-MSh) algorithm is introduced to adaptively calculate the optimal DL. Also, two methods based on the coherence factor (CF) are proposed to determine the subarray length in the spatial smoothing and the number of samples required for temporal averaging. The performance of the proposed methods is evaluated using simulated and experimental RF data. It is shown that the methods preserve the contrast and improve the resolution by about 35% and 38% compared to the MV having a fix loading coefficient and the MV-Sh algorithm.

Minimum Variance Combined With Modified Delay Multiply-and-Sum Beamforming for Plane-Wave Compounding

Plane-wave compounding is an active topic of research in ultrasound imaging because it is a promising technique for ultrafast ultrasound imaging. Unfortunately, due to the data-independent nature of the traditional compounding method, it imposes a fundamental limit on image quality. To address this issue, adaptive beamformers have been implemented in the compounding procedure. In this article, a new adaptive beamformer for the 2-D data set obtained from multiple plane-wave transmissions is investigated. In the proposed scheme, the minimum variance (MV) weights are applied to the backscattered echoes. Then, the final image is obtained by employing a modified version of the delay multiply-and-sum (DMAS) beamformer in the coherent compounding. The results demonstrate that the presented MV-DMAS scheme outperforms the conventional coherent compounding in both terms of resolution and contrast. It also offers improvements over the 2-D-DMAS and some MV-based methods presented in the literature, such that it achieves at least 20.9% enhancement in sidelobe reduction compared with the best result of MV-based methods. Also, by the proposed method, the in vivo study shows an improved generalized contrast-to-noise ratio (GCNR) that implies a higher probability of lesion detection.

Joint Generalized Coherence Factor and Minimum Variance Beamformer for Synthetic Aperture Ultrasound Imaging

The delay-and-sum (DAS) beamformer is the most commonly used method in medical ultrasound imaging. Compared with the DAS beamformer, the minimum variance (MV) beamformer has an excellent ability to improve lateral resolution by minimizing the output of interference and noise power. However, it is hard to overcome the tradeoff between satisfactory lateral resolution and speckle preservation performance due to the fixed subarray length of covariance matrix estimation. In this study, a new approach for MV beamforming with adaptive spatial smoothing is developed to address this problem. In the new approach, the generalized coherence factor (GCF) is used as a local coherence detection tool to adaptively determine the subarray length for spatial smoothing, which is called adaptive spatial-smoothed MV (AMV). Furthermore, another adaptive regional weighting strategy based on the local signal-to-noise ratio (SNR) and GCF is devised for AMV to enhance the image contrast, which is called GCF regional weighted AMV (GAMV). To evaluate the performance of the proposed methods, we compare them with the standard MV by conducting the simulation, in vitro experiment, and the in vivo rat mammary tumor study. The results show that the proposed methods outperform MV in speckle preservation without an appreciable loss in lateral resolution. Moreover, GAMV offers excellent performance in image contrast. In particular, AMV can achieve maximal improvements of speckle signal-to-noise ratio (SNR) by 96.19% (simulation) and 62.82% (in vitro) compared with MV. GAMV achieves improvements of contrast-to-noise ratio by 27.16% (simulation) and 47.47% (in vitro) compared with GCF. Meanwhile, the losses in lateral resolution of AMV are 0.01 mm (simulation) and 0.17 mm (in vitro) compared with MV. Overall, this indicates that the proposed methods can effectively address the inherent limitation of the standard MV in order to improve the image quality.

High Resolution Minimum Variance Beamformer With Low Complexity in Medical Ultrasound Imaging

Although the minimum variance beamformer (MVB) shows a significant improvement in resolution and contrast in medical ultrasound imaging, its high computational complexity is a major problem in a real-time imaging system. Therefore, it seems necessary to propose a new method with a lower computational complexity that preserves the advantages of the MVB. In this paper, the MVB was implemented with a partial generalized sidelobe canceler (GSC) with a blocking matrix based on our previous study, which projected the incoming signals to a lower dimensional space. The partial GSC separated the weight vector into one fixed and one adaptive weight, whereby the optimization could be performed with lower complexity on the adaptive part. In addition, this dimension reduction allowed us to increase the length of the subarray when using a spatial smoothing method, which was used to decorrelate the incoming signals. The subarray length was limited to half the length of the full array size in the ordinary MVB, while the proposed beamformer could cross over this limitation. The results demonstrated that the point spread function of the proposed beamformer was about 6.3 times narrower than the classic MVB, while the contrast was almost saved. These results were achieved with linear computational complexity by the proposed method, while it was cubic for the MVB. For a sample scenario, the proposed method needed only 1.8% of the required ops of the MVB.

Resolving Ultrasound Contrast Microbubbles Using Minimum Variance Beamforming

Minimum Variance (MV) beamforming is known to improve the lateral resolution of ultrasound images and enhance the separation of isolated point scatterers. This paper aims to evaluate the adaptive beamformer's performance with flowing microbubbles (MBs) which are relevant to super-resolution ultrasound imaging. Simulations using point scatterer data from single emissions were complemented by an experimental investigation performed using a capillary tube phantom and the Synthetic Aperture Real-time Ultrasound System (SARUS). The MV performance was assessed by the minimum distance that allows the display of two scatterers positioned side-by-side, the lateral Full-Width-at-Half-Maximum (FWHM), and the Peak-Sidelobe-Level (PSL). In the tube, scatterer responses separated by down to [Formula: see text] (or 1.05λ ) were distinguished by the MV method, while the standard Delay-And-Sum (DAS) beamformers were unable to achieve such separation. Up to ninefold FWHM decrease was also measured in favor of the MV beamformer for individual echoes from MBs. The lateral distance between two scatterers impacted on their FWHM value, and additional differences in the scatterers' axial or out-of-plane position also impacted on their size and appearance. The simulation and experimental results were in agreement in terms of lateral resolution. The point scatterer study showed that the proposed MV imaging scheme provided clear resolution benefits compared to DAS. Current super-resolution methods mainly depend on DAS beamformers. Instead, the use of the MV method may provide a larger number of detected, and potentially better localized, MB scatterers.

Sidelobe reduction for plane wave compounding with a limited frame number

BACKGROUND

In ultrasound plane wave imaging (PWI), image details are often blurred by the off-axis artefacts resulting from high sidelobe. Recently plane wave compounding (PWC) is proposed as a promising technique for the sidelobe suppression in the PWI. However, its high demand for the frame number results in an obvious frame rate loss, which is intolerable in the ultrafast imaging modality. To reduce the number of frames required for compounding, coherence in the compounding frames should be exploited.

METHODS

In this paper, we propose a global effective distance-based sidelobe suppressing method for the PWC with a limited frame number, where the global effective distance is introduced to measure the inter-frame coherence. Specifically, the effective distance is firstly computed by using a sparse representation-based algorithm. Then, the sidelobe localization is carried out on the basis of the effective distance. Finally, the target-dependent weighting factor is adopted to suppress the sidelobe.

RESULTS

To assert the superiority of our proposed method, we compare the performances of different sidelobe reduction methods on both simulated and experimental PWC data. In case of 5 steering angles, our method shows a 19 dB reduction in the peak sidelobe level compared to the normal PWC in the point spread function test, and the contrast ratio is enhanced by more than 10% in both the simulation and phantom studies.

CONCLUSIONS

Consequently, the proposed method is convinced to be a promising approach in enhancing the PWC image quality.

A Spatial Coherence Approach to Minimum Variance Beamforming for Plane-Wave Compounding

A new approach to implement minimum variance distortionless response (MVDR) beamforming is introduced for coherent plane-wave compounding (CPWC). MVDR requires the covariance matrix of the incoming signal to be estimated and a spatial smoothing approximation is usually adopted to prevent this calculation from being underconstrained. In the new approach, we analyze MVDR as a spatial filter that decorrelates signals received at individual channels before summation. Based on the analysis, we develop two MVDR beamformers without using any spatial smoothing. First, MVDR weights are applied to the received signals after accumulating the data over transmits at different angles, while the second involves weighting the data collected in individual transmits and compounding over the transducer elements. In both cases, the covariance matrix is estimated using a set of slightly different combinations of the echo data. We show the sufficient statistic for this estimation that can be described by approximating the correlation among the backscattered ultrasound signals to their spatial coherence. Using the van Cittert-Zernike theorem, their statistical similarity is assessed by relating the spatial coherence to the profile of the source intensity. Both spatial-coherence-based MVDR beamformers are evaluated on data sets acquired from simulation, phantom, and in vivo studies. Imaging results show that they offer improvements over simple coherent compounding in terms of spatial and contrast resolutions. They also outperform other existing MVDR-based methods in the literature that are applied to CPWC.

Ultrafast Ultrasound Imaging Using Combined Transmissions With Cross-Coherence-Based Reconstruction

Plane-wave-based ultrafast imaging has become the prevalent technique for non-conventional ultrasound imaging. The image quality, especially in terms of the suppression of artifacts, is generally compromised by reducing the number of transmissions for a higher frame rate. We hereby propose a new ultrafast imaging framework that reduces not only the side lobe artifacts but also the axial lobe artifacts using combined transmissions with a new coherence-based factor. The results from simulations, in vitro wire phantoms, the ex vivo porcine artery, and the in vivo porcine heart show that our proposed methodology greatly reduced the axial lobe artifact by 25±5 dB compared with coherent plane-wave compounding (CPWC), which was considered as the ultrafast imaging standard, and suppressed side lobe artifacts by 15 ± 5 dB compared with CPWC and coherent spherical-wave compounding. The reduction of artifacts in our proposed ultrafast imaging framework led to a better boundary delineation of soft tissues than CPWC.

Enhanced linear-array photoacoustic beamforming using modified coherence factor

Photoacoustic imaging (PAI) is a promising medical imaging modality providing the spatial resolution of ultrasound imaging and the contrast of optical imaging. For linear-array PAI, a beamformer can be used as the reconstruction algorithm. Delay-and-sum (DAS) is the most prevalent beamforming algorithm in PAI. However, using DAS beamformer leads to low-resolution images as well as high sidelobes due to nondesired contribution of off-axis signals. Coherence factor (CF) is a weighting method in which each pixel of the reconstructed image is weighted, based on the spatial spectrum of the aperture, to mainly improve the contrast. We demonstrate that the numerator of the formula of CF contains a DAS algebra and propose the use of a delay-multiply-and-sum beamformer instead of the available DAS on the numerator. The proposed weighting technique, modified CF (MCF), has been evaluated numerically and experimentally compared to CF. It was shown that MCF leads to lower sidelobes and better detectable targets. The quantitative results of the experiment (using wire targets) show that MCF leads to for about 45% and 40% improvement, in comparison with CF, in the terms of signal-to-noise ratio and full-width-half-maximum, respectively.

Improvements to ultrasonic beamformer design and implementation derived from the task-based analytical framework

The task-based framework, previously developed for beamformer comparison [Nguyen, Prager, and Insana, J. Acoust. Soc. Am. 140, 1048-1059 (2016)], is extended to design a new beamformer with potential applications in breast cancer diagnosis. The beamformer is based on a better approximation of the Bayesian strategy. It is a combination of the Wiener-filtered beamformer and an iterative process that adapts the generated image to specific features of the object. Through numerical studies, the new method is shown to outperform other beamformers drawn from the framework, but at an increase in computational cost. It requires a preprocessing step where the scattering field is segmented into regions with distinct statistical properties. Segmentation errors become a major limitation to the beamformer performance. All the beamformers under investigation are tested using data obtained from an instrumented ultrasound machine. They are implemented using a new time delay calculation, recently developed in the pixel-based beamforming studies presented here, which helps to overcome the challenge posed by the shift-variant nature of the imaging system. The efficacy of each beamformer is evaluated based on the quality of generated images in the context of the task-based framework. The in vitro results confirm the conclusions drawn from the simulations.

Ultrasound Pixel-Based Beamforming With Phase Alignments of Focused Beams

We previously developed unified pixel-based (PB) beamforming to generate high-resolution sonograms, based on field pattern analysis. In this framework, we found that the transmit waveshape away from the focus could be characterized by two spherical pulses. These correspond to the maximal and minimal distances from the imaging point to the active aperture. The beamformer uses this model to select the highest energy signals from backscattered data. A spatiotemporal interpolation formula is used to provide a smooth transition in regions near the focal depth where there is no dominant reflected pulse. In this paper, we show that the unified PB approach is less robust at lower center frequencies. The interpolated data is suboptimal for a longer transmit waveshape. As a result, the spatial resolution at the focal depth is lower than that in other regions. By further exploring the field pattern, we propose a beamformer that is more robust to variations in beamwidth. The new method, named coherent PB beamforming, aligns and compounds the pulse data directly in the transition regions. In simulation and phantom studies, the coherent PB approach is shown to outperform the unified PB approach in spatial resolution. It helps regain optimal resolution at the focal depth while still maintaining good image quality in other regions. We also demonstrate the new method on in vivo data where its improvements over the unified PB method are demonstrated on scanned objects with a more complicated structure.

Double-Stage Delay Multiply and Sum Beamforming Algorithm: Application to Linear-Array Photoacoustic Imaging

Photoacoustic imaging (PAI) is an emerging medical imaging modality capable of providing high spatial resolution of Ultrasound (US) imaging and high contrast of optical imaging. Delay-and-Sum (DAS) is the most common beamforming algorithm in PAI. However, using DAS beamformer leads to low resolution images and considerable contribution of off-axis signals. A new paradigm namely delay-multiply-and-sum (DMAS), which was originally used as a reconstruction algorithm in confocal microwave imaging, was introduced to overcome the challenges in DAS. DMAS was used in PAI systems and it was shown that this algorithm results in resolution improvement and sidelobe degrading. However, DMAS is still sensitive to high levels of noise, and resolution improvement is not satisfying. Here, we propose a novel algorithm based on DAS algebra inside DMAS formula expansion, double stage DMAS (DS-DMAS), which improves the image resolution and levels of sidelobe, and is much less sensitive to high level of noise compared to DMAS. The performance of DS-DMAS algorithm is evaluated numerically and experimentally. The resulted images are evaluated qualitatively and quantitatively using established quality metrics including signal-to-noise ratio (SNR), full-width-half-maximum (FWHM) and contrast ratio (CR). It is shown that DS-DMAS outperforms DAS and DMAS at the expense of higher computational load. DS-DMAS reduces the lateral valley for about 15 dB and improves the SNR and FWHM better than 13% and 30%, respectively. Moreover, the levels of sidelobe are reduced for about 10 dB in comparison with those in DMAS.