A blind deconvolution approach to ultrasound imaging

Deconvolution based on sparsity and continuity improves the quality of ultrasound image

The application of ultrasound (US) image has been limited by its limited resolution, inherent speckle noise, and the impact of clutter and artifacts, especially in the miniaturized devices with restricted hardware conditions. In order to solve these problems, many researchers have explored a number of hardware modifications as well as algorithmic improvements, but further improvements in resolution, signal-to-noise ratio (SNR) and contrast are still needed. In this paper, a deconvolution algorithm based on sparsity and continuity (DBSC) is proposed to obtain the higher resolution, SNR, and, contrast. The algorithm begins with a relatively bold Wiener filtering for initial enhancement of image resolution in preprocessing, but it also introduces ringing noise and compromises the SNR. In further processing, the noise is suppressed based on the characteristic that the adjacent pixels of the US image are continuous as long as Nyquist sampling criterion is met, and the extraction of high-frequency information is balanced by using relatively sparse. Subsequently, the theory and experiments demonstrate that relative sparsity and continuity are general properties of US images. DBSC is compared with other deconvolution strategies through simulations and experiments, and US imaging under different transmission channels is also investigated. The final results show that the proposed method can greatly improve the resolution, as well as provide significant advantages in terms of contrast and SNR, and is also feasible in applications to devices with limited hardware.

The Performance Improvement of Ultrasound Localization Microscopy (ULM) Using the Robust Principal Component Analysis (RPCA)

This paper presents an algorithm for ultrafast ultrasound localization microscopy (ULM) used for the detection, localization, accumulation, and rendering of intravenously injected ultrasound contrast agents (UCAs) enabling to yield hemodynamic maps of the brain microvasculature. It consists in integrating a robust principal component analysis (RPCA)-based approach into the ULM process for more robust tissue filtering, resulting in more accurate ULM images. Numerical experiments conducted on an in vivo rat brain perfusion dataset demonstrate the efficiency of the proposed approach compared to the most widely used state-of-the-art method.

Image enhancement in acoustic-resolution photoacoustic microscopy enabled by a novel directional algorithm

By considering the line pattern of acoustic-resolution photoacoustic microscopy (AR-PAM) vessel images, we develop modified algorithms for synthetic aperture focusing technique (SAFT) and deconvolution based on a directional approach to enhance images. The modified algorithms consist of Fourier accumulation SAFT (FA-SAFT) and directional model-based (D-MB) deconvolution. To evaluate the performance of our algorithms, we conduct a series of imaging experiments and apply our algorithms, and existing SAFT and deconvolution algorithms are also applied for side-by-side comparison. By imaging tungsten wire phantom, our algorithms enable full width at half maximum of 26 - 31 µm over depth of focus of 1.8 mm and minimum resolvable distance of 46 - 49 µm, besting existing SAFT and deconvolution algorithms. Imaging of leaf skeleton phantom and in vivo imaging of mouse blood vessels also prove that our algorithm is capable of providing high-resolution, high-signal-to-noise ratio, and good-fidelity results for complex structures and for in vivo applications, especially for the images with the line pattern. The proposed directional approach can not only be used in AR-PAM but also in other imaging modalities to deal with the line pattern, such as FA-SAFT for ultrasound imaging and D-MB deconvolution for optical coherence tomography angiography.

Variational Formulation of Unsupervised Deep Learning for Ultrasound Image Artifact Removal

Recently, deep learning approaches have been successfully used for ultrasound (US) image artifact removal. However, paired high-quality images for supervised training are difficult to obtain in many practical situations. Inspired by the recent theory of unsupervised learning using optimal transport driven CycleGAN (OT-CycleGAN), here, we investigate the applicability of unsupervised deep learning for US artifact removal problems without matched reference data. Two types of OT-CycleGAN approaches are employed: one with the partial knowledge of the image degradation physics and the other with the lack of such knowledge. Various US artifact removal problems are then addressed using the two types of OT-CycleGAN. Experimental results for various unsupervised US artifact removal tasks confirmed that our unsupervised learning method delivers results comparable to supervised learning in many practical applications.

Approximate back-projection method for improving lateral resolution in circular-scanning-based photoacoustic tomography

PURPOSE

In circular-scanning-based photoacoustic tomography (PAT), the effect of finite transducer aperture has not been effectively resolved. The goal of this paper is to propose a practical reconstruction method that accounts for the finite transducer aperture to improve the lateral resolution.

METHODS

We for the first time propose to calculate the spatial-temporal response (STR) of the employed finite-sized transducer in a forward model, and then compensate the time delay and the directional sensitivity of the transducer in the framework of the back-projection method. Both simulation and phantom experiments were carried out to evaluate the lateral resolution improvement with the proposed method. The performance of this new method for imaging complicated targets was also assessed by calculating the mean image gradient.

RESULTS

Simulation results showed that with this new method the lateral resolution for off-center targets can be as good as that for the center targets. Phantom experimental results showed that this new method can improve the lateral resolution more than two times for a point target about 5 mm far from the rotation center. Phantom experimental results also showed that many blurred fine structures of a piece of leaf veins at the off-center regions were well restored with the new method, and the mean image gradient improved about 1.3 times.

CONCLUSION

The proposed new method can effectively account for the effect of finite transducer aperture for circular-scanning-based PAT in homogenous acoustic media. This new method also features its robustness and computational efficiency, so that it is a worthy replacement to the conventional back-projection algorithm in circular-scanning-based PAT. This new method can be of great importance to the design of circular-scanning or spherical-scanning-based PAT systems.

Ultrasound Image Deconvolution Using Fundamental and Harmonic Images

Ultrasound (US) image restoration from radio frequency (RF) signals is generally addressed by deconvolution techniques mitigating the effect of the system point spread function (PSF). Most of the existing methods estimate the tissue reflectivity function (TRF) from the so-called fundamental US images, based on an image model assuming the linear US wave propagation. However, several human tissues or tissues with contrast agents have a nonlinear behavior when interacting with US waves leading to harmonic images. This work takes this nonlinearity into account in the context of TRF restoration, by considering both fundamental and harmonic RF signals. Starting from two observation models (for the fundamental and harmonic images), TRF estimation is expressed as the minimization of a cost function defined as the sum of two data fidelity terms and one sparsity-based regularization stabilizing the solution. The high attenuation with a depth of harmonic echoes is integrated into the direct model that relates the observed harmonic image to the TRF. The interest of the proposed method is shown through synthetic and in vivo results and compared with other restoration methods.

Axial super-resolution in ultrasound imaging with application to non-destructive evaluation

A fundamental challenge in non-destructive evaluation using ultrasound is to accurately estimate the thicknesses of different layers or cracks present in the object under examination, which implicitly corresponds to accurately localizing the point-sources of the reflections from the measured signal. Conventional signal processing techniques cannot overcome the axial-resolution limit of the ultrasound imaging system determined by the wavelength of the transmitted pulse. In this paper, starting from the solution to the 1-D wave equation, we show that the ultrasound reflections could be effectively modeled as finite-rate-of-innovation (FRI) signals. The FRI modeling approach is a new paradigm in signal processing. Apart from allowing for the signals to be sampled below the Nyquist rate, the FRI framework also transforms the reconstruction problem into one of parametric estimation. We employ high-resolution parametric estimation techniques to solve the problem. We demonstrate axial super-resolution capability (resolution below the theoretical limit) of the proposed technique both on simulated as well as experimental data. A comparison of the FRI technique with time-domain and Fourier-domain sparse recovery techniques shows that the FRI technique is more robust. We also assess the resolvability of the proposed technique under different noise conditions on data simulated using the Field-II software and show that the reconstruction technique is robust to noise. For experimental validation, we consider Teflon sheets and Agarose phantoms of varying thicknesses. The experimental results show that the FRI technique is capable of super-resolving by a factor of three below the theoretical limit.

Application of Blind Deconvolution Based on the New Weighted L1-norm Regularization with Alternating Direction Method of Multipliers in Light Microscopy Images

This study aimed to develop and evaluate a blind-deconvolution framework using the alternating direction method of multipliers (ADMMs) incorporated with weighted L1-norm regularization for light microscopy (LM) images. A presimulation study was performed using the Siemens star phantom prior to conducting the actual experiments. Subsequently, the proposed algorithm and a total generalized variation-based (TGV-based) method were applied to cross-sectional images of a mouse molar captured at 40× and 400× on-microscope magnifications and the results compared, and the resulting images were compared. Both simulation and experimental results confirmed that the proposed deblurring algorithm effectively restored the LM images, as evidenced by the quantitative evaluation metrics. In conclusion, this study demonstrated that the proposed deblurring algorithm can efficiently improve the quality of LM images.

Air-Coupled Ultrasound Time Reversal (ACU-TR) For Subwavelength Nondestructive Imaging

Air-coupled ultrasound (ACU) is increasingly used for nondestructive testing (NDT). With ACU, no contact or coupling agent (e.g., water and ultrasound gel) is needed between transducers and test sample, which provides high measurement reproducibility. However, for testing in production, a minimum separation is often necessary between the sample and the transducers to avoid contamination or transducer damage. Due to wave diffraction, the collimation of the ultrasound beam decreases for larger propagation distances, and ACU images become blurred and show lower defect lateral resolution with increasing sample-transducer separation. This is especially critical to thick composites, where large-size planar sources are used to bridge the large ACU transmission loss with good collimation. In this work, ACU reradiation in unbounded media is extended to NDT of multilayered composites. The extended method is named ACU time reversal (ACU-TR) and significantly improves the defect resolution of ACU imaging. With ACU-TR, the complete pressure distribution radiated by large ACU source is measured with point receivers (RXs) in one plane arbitrarily separated from the sample. By applying acoustic holography physics, it is then possible to quantitatively reconstruct the pressure field directly at arbitrary sample defect planes, which compensates for undesired diffraction phenomena and improves minimum detectable defect size, thereby achieving subwavelength lateral resolution. We tested the method on complex wood-based composite samples based on the ACU far-field measurements at a separation of 160 mm between the sample and the RX transducer. With the proposed method, it is possible to detect surface defects as well as inner defects within composite boards. In the future, by using point RX arrays instead of a scanned microphone, both data acquisition and evaluation can be potentially implemented in real time.

Point Spread Function Formation in Plane-Wave Imaging: A Theoretical Approximation in Fourier Migration

The point spread function (PSF) is often analyzed to determine the image quality of an ultrasound system. The formation of PSF is determined by practical factors, such as transducer aperture, element directivity, apodization, pitch, imaging position, and steering angle. Conventional numerical simulations provide an iterative approach to examine those factors' effects but cannot explain the inherent mechanism of PSF formation. This article presents a theoretical approximation of PSF formation for plane-wave imaging throughout the Fourier-based reconstruction process. Aforementioned factors are incorporated in the theory. The proposed theory is used to analyze the effects of those factors and presents a high degree of consistency with numerical simulations and experiments.

A Novel 2-D Synthetic Aperture Focusing Technique for Acoustic-Resolution Photoacoustic Microscopy

Acoustic-resolution photoacoustic microscopy (AR-PAM) is a promising technology for vascular or tumor-targeted molecular imaging. Unique advantages of AR-PM are its non-invasive, non-ionizing real-time, and deeper imaging depth. AR-PAM typically uses an ultrasound transducer with a high acoustic numerical aperture (NA) to enable deeper imaging depth. While high NA achieves good lateral resolution in the focal plane but significantly degrades the lateral resolution in the out-of-focus region. Synthetic aperture focusing technique (SAFT) has been introduced to overcome this out-of-focus degradation by synthesizing the correlated signals. Several 2-D SAFTs have been also reported to improve degraded resolution in all directions. However, the resolution enhancement of the previously reported 2-D SAFTs are suboptimal and are not equivalent to the 1-D SAFT performance under an ideal condition with the sample orientation perpendicular to the synthetic aperture direction. In this paper, we present a new 2-D SAFT called 2-D directional SAFT that improves the lateral resolution significantly and we compare our results against 1-D SAFT under ideal condition. We applied this algorithm to phantom and in vivo images to show the improvement in image quality. We also implement this algorithm in a graphical processing unit to achieve high performance to show the practicality of implementing this new algorithm in a system.

An improved Richardson-Lucy iterative algorithm for C-scan image restoration and inclusion size measurement

The accuracy of measuring inclusion size in direct C-scan image of immersion ultrasonic testing is restricted by the lateral resolution of the focused transducer, even if a high frequency is used, and the blurred edge due to scattering of sound waves at inclusions. In this work, an improved image restoration method that is based on the Richardson-Lucy (RL) iterative algorithm is proposed, which is used to restore the C-scan image and improve the accuracy of inclusion size measurement in immersion ultrasonic testing. For the improved RL iterative algorithm, the point spread function (PSF) is derived based on the multi-Gaussian beam model and Kirchhoff approximation, which considers the propagation properties of sound waves at water-steel interface and the spectral characteristics of the transducer with high frequency. In order to determine the final iteration number, the relationship between final iteration number and size of the inclusion in the image is established by restoring the simulated C-scan image and further calibrated with size correction factor. The size correction factor considers the effect of sound attenuation and electro-mechanical transformation encountered in practical testing equipment. Experimental results show that the inclusion sizes measured in restored C-scan images agree well with the optical micrograph results, which prove the effectiveness of the proposed method.

Bubble-echo based deconvolution of contrast-enhanced ultrasound imaging: Simulation and experimental validations

PURPOSE

Improvement of both the imaging resolution and the contrast-to-tissue ratio (CTR) is a current emphasis of contrast-enhanced ultrasound (CEUS) for microvascular perfusion imaging. Based on the strong nonlinear characteristics of contrast agents, the CTRs have been significantly enhanced using various advanced CEUS methods. However, the imaging resolution of these methods is limited by the finite bandwidth of the imaging process. This study aimed to propose a bubble-echo based deconvolution (BED) method for CEUS with both improved resolution and CTR.

METHOD

The method is built on a modified convolution model and uses novel bubble-echo based point-spread-functions to reconstruct the images by regularized inverse Wiener filtering. Performances of the proposed BED for three CEUS modes are investigated through simulations and in vivo perfusion experiments.

RESULTS

BED of fundamental imaging was found to have the highest improvement in imaging resolution with the resolution gain up to 2.0 ± 0.2 times, which was comparable to the approved cepstrum-based deconvolution (CED). BED of second-harmonic imaging had the best performance in CTR with an enhancement of 9.8 ± 2.3 dB, which was much higher than CED. Pulse inversion BED had both a better resolution and a higher CTR.

CONCLUSION

All results indicate that BED could obtain CEUS image with both an improved resolution and a high CTR, which has important significance to microvascular perfusion evaluation in deep tissue.

Design and Characterization of an Acoustically and Structurally Matched 3-D-Printed Model for Transcranial Ultrasound Imaging

For investigating human transcranial ultrasound imaging (TUI) through the temporal bone, an intact human skull is needed. Since it is complex and expensive to obtain one, it requires that experiments are performed without excision or abrasion of the skull. Besides, to mimic blood circulation for the vessel target, cellulose tubes generally fit the vessel simulation with straight linear features. These issues, which limit experimental studies, can be overcome by designing a 3-D-printed skull model with acoustic and dimensional properties that match a real skull and a vessel model with curve and bifurcation. First, the optimal printing material which matched a real skull in terms of the acoustic attenuation coefficient and sound propagation velocity was identified at 2-MHz frequency, i.e., 7.06 dB/mm and 2168.71 m/s for the skull while 6.98 dB/mm and 2114.72 m/s for the printed material, respectively. After modeling, the average thickness of the temporal bone in the printed skull was about 1.8 mm, while it was to 1.7 mm in the real skull. Then, a vascular phantom was designed with 3-D-printed vessels of low acoustic attenuation (0.6 dB/mm). It was covered with a porcine brain tissue contained within a transparent polyacrylamide gel. After characterizing the acoustic consistency, based on the designed skull model and vascular phantom, vessels with inner diameters of 1 and 0.7 mm were distinguished by resolution enhanced imaging with low frequency. Measurements and imaging results proved that the model and phantom are authentic and viable alternatives, and will be of interest for TUI, high intensity focused ultrasound, or other therapy studies.

EEMD Domain AR Spectral Method for Mean Scatterer Spacing Estimation of Breast Tumors From Ultrasound Backscattered RF Data

We present a novel method for estimating the mean scatterer spacing (MSS) of breast tumors using ensemble empirical mode decomposition (EEMD) domain analysis of deconvolved backscattered radio frequency (RF) data. The autoregressive (AR) spectrum from which the MSS is estimated is obtained from the intrinsic mode functions (IMFs) due to regular scatterers embedded in RF data corrupted by the diffuse scatterers. The IMFs are chosen by giving priority to the presence of an enhanced fundamental harmonic and the presence of a greater number of higher harmonics in the AR spectrum estimated from the IMFs. The AR model order is chosen by minimizing the mean absolute percentage error (MAPE) criterion. In order to ensure that the backscattered data is indeed from a source of coherent scattering, we begin by performing a non-parametric Kolmogorov-Smirnov (K-S) classification test on the backscattered RF data. Deconvolution of the backscattered RF data, which have been classified by the K-S test as sources of significant coherent scattering, is done to reduce the system effect. EEMD domain analysis is then performed on the deconvolved data. The proposed method is able to recover the harmonics associated with the regular scatterers and overcomes many problems encountered while estimating the MSS from the AR spectrum of raw RF data. Using our technique, a mean absolute percentage error (MAPE) of 5.78% is obtained while estimating the MSS from simulated data, which is lower than that of the existing techniques. Our proposed method is shown to outperform the state of the art techniques, namely, singular spectrum analysis, generalized spectrum (GS), spectral autocorrelation (SAC), and modified SAC for different simulation conditions. The MSS for in vivo normal breast tissue is found to be 0.69 ± 0.04 mm; for benign and malignant tumors it is found to be 0.73 ± 0.03 and 0.79 ± 0.04 mm, respectively. The separation between the MSS values of normal and benign tissues for our proposed method is similar to the separations obtained for the conventional methods, but the separation between the MSS values for benign and malignant tissues for our proposed method is slightly higher than that for the conventional methods. When the MSS is used to classify breast tumors into benign and malignant, for a threshold-based classifier, the increase in specificity, accuracy, and area under curve are 18%, 19%, and 22%, respectively, and that for statistical classifiers are 9%, 13%, and 19%, respectively, from that of the next best existing technique.

Pulse-Inversion Subharmonic Ultrafast Active Cavitation Imaging in Tissue Using Fast Eigenspace-Based Adaptive Beamforming and Cavitation Deconvolution

Pulse-inversion subharmonic (PISH) imaging can display information relating to pure cavitation bubbles while excluding that of tissue. Although plane-wave-based ultrafast active cavitation imaging (UACI) can monitor the transient activities of cavitation bubbles, its resolution and cavitation-to-tissue ratio (CTR) are barely satisfactory but can be significantly improved by introducing eigenspace-based (ESB) adaptive beamforming. PISH and UACI are a natural combination for imaging of pure cavitation activity in tissue; however, it raises two problems: 1) the ESB beamforming is hard to implement in real time due to the enormous amount of computation associated with the covariance matrix inversion and eigendecomposition and 2) the narrowband characteristic of the subharmonic filter will incur a drastic degradation in resolution. Thus, in order to jointly address these two problems, we propose a new PISH-UACI method using novel fast ESB (F-ESB) beamforming and cavitation deconvolution for nonlinear signals. This method greatly reduces the computational complexity by using F-ESB beamforming through dimensionality reduction based on principal component analysis, while maintaining the high quality of ESB beamforming. The degraded resolution is recovered using cavitation deconvolution through a modified convolution model and compressive deconvolution. Both simulations and in vitro experiments were performed to verify the effectiveness of the proposed method. Compared with the ESB-based PISH-UACI, the entire computation of our proposed approach was reduced by 99%, while the axial resolution gain and CTR were increased by 3 times and 2 dB, respectively, confirming that satisfactory performance can be obtained for monitoring pure cavitation bubbles in tissue erosion.

Enhanced axial and lateral resolution using stabilized pulses

Ultrasound B-scan imaging systems operate under some well-known resolution limits. To improve resolution, the concept of stable pulses, having bounded inverse filters, was previously utilized for the lateral deconvolution. This framework has been extended to the axial direction, enabling a two-dimensional deconvolution. The modeling of the two-way response in the axial direction is discussed, and the deconvolution is performed in the in-phase quadrature data domain. Stable inverse filters are generated and applied for the deconvolution of the image data from Field II simulation, a tissue-mimicking phantom, and in vivo imaging of a carotid artery, where resolution enhancement is observed. Specifically, in simulation results, the resolution is enhanced by as many as 8.75 times laterally and 20.5 times axially considering the [Formula: see text] width of the autocorrelation of the envelope images.

Enhanced axial and lateral resolution using stabilized pulses

Ultrasound B-scan imaging systems operate under some well-known resolution limits. To improve resolution, the concept of stable pulses, having bounded inverse filters, was previously utilized for the lateral deconvolution. This framework has been extended to the axial direction, enabling a two-dimensional deconvolution. The modeling of the two-way response in the axial direction is discussed, and the deconvolution is performed in the in-phase quadrature data domain. Stable inverse filters are generated and applied for the deconvolution of the image data from Field II simulation, a tissue-mimicking phantom, and in vivo imaging of a carotid artery, where resolution enhancement is observed. Specifically, in simulation results, the resolution is enhanced by as many as 8.75 times laterally and 20.5 times axially considering the [Formula: see text] width of the autocorrelation of the envelope images.

Photoacoustic microscopy in vivo using synthetic-aperture focusing technique combined with three-dimensional deconvolution

Acoustic-resolution photoacoustic microscopy (ARPAM) plays an important role in studying the microcirculation system of biological tissues with deep penetration. High lateral resolution of ARPAM is achieved by using a high numerical aperture acoustic transducer. The deteriorated lateral resolution in the out-of-focus region can be alleviated by synthetic aperture focusing technique (SAFT). Previously, we reported a three-dimensional (3D) deconvolution ARPAM to improve both lateral and axial resolutions in the focus region. In this study, we present our extension of resolution enhancement to the out-of-focus region based on two-dimensional SAFT combined with the 3D deconvolution (SAFT+Deconv). In both the focus and out-of-focus regions, depth-independent lateral resolution provided by SAFT, together with inherently depth-independent axial resolution, ensures a depth-independent point spread function for 3D deconvolution algorithm. Imaging of 10 μm polymer beads shows that SAFT+Deconv ARPAM improves the -6 dB lateral resolutions from 65-700 μm to 20-29 μm, and the -6 dB axial resolutions from 35-42 μm to 12-19 μm in an extended depth of focus (DOF) of ∼2 mm. The signal-to-noise ratio is also increased by 6-30 dB. The resolution enhancement in three dimensions is validated by in vivo imaging of a mouse's dorsal subcutaneous microvasculature. Our results suggest that SAFT+Deconv ARPAM may allow fine spatial resolution with deep penetration and extended DOF for biomedical photoacoustic applications.

Increasing Axial Resolution of Ultrasonic Imaging With a Joint Sparse Representation Model

The axial resolution of ultrasonic imaging is confined by the temporal width of acoustic pulse generated by the transducer, which has a limited bandwidth. Deconvolution can eliminate this effect and, therefore, improve the resolution. However, most ultrasonic imaging methods perform deconvolution scan line by scan line, and therefore the information embedded within the neighbor scan lines is unexplored, especially for those materials with layered structures such as blood vessels. In this paper, a joint sparse representation model is proposed to increase the axial resolution of ultrasonic imaging. The proposed model combines the sparse deconvolution along the axial direction with a sparsity-favoring constraint along the lateral direction. Since the constraint explores the information embedded within neighbor scan lines by connecting nearby pixels in the ultrasound image, the axial resolution of the image improves after deconvolution. The results on simulated data showed that the proposed method can increase resolution and discover layered structure. Moreover, the results on real data showed that the proposed method can measure carotid intima-media thickness automatically with good quality ( 0.56±0.03 versus 0.60±0.06 mm manually).

Beamforming Through Regularized Inverse Problems in Ultrasound Medical Imaging

Beamforming (BF) in ultrasound (US) imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum (DAS) is still extensively used nowadays in clinical applications, due to its real-time capabilities. The most common alternatives are minimum variance (MV) method and its variants, which overcome the drawbacks of DAS, at the cost of higher computational complexity that limits its utilization in real-time applications. In this paper, we propose to perform BF in US imaging through a regularized inverse problem based on a linear model relating the reflected echoes to the signal to be recovered. Our approach presents two major advantages: 1) its flexibility in the choice of statistical assumptions on the signal to be beamformed (Laplacian and Gaussian statistics are tested herein) and 2) its robustness to a reduced number of pulse emissions. The proposed framework is flexible and allows for choosing the right tradeoff between noise suppression and sharpness of the resulted image. We illustrate the performance of our approach on both simulated and experimental data, with in vivo examples of carotid and thyroid. Compared with DAS, MV, and two other recently published BF techniques, our method offers better spatial resolution, respectively contrast, when using Laplacian and Gaussian priors.

Generalized LASSO with under-determined regularization matrices

This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form via the Lagrangian framework. In addition, we show that some published results of LASSO can be extended to the generalized LASSO, and some variants of LASSO, e.g., robust LASSO, can be rewritten into the generalized LASSO form and hence can be transformed into basic LASSO. Based on this connection, many existing results concerning LASSO, e.g., efficient LASSO solvers, can be used for generalized LASSO.

Reconstruction of Enhanced Ultrasound Images From Compressed Measurements Using Simultaneous Direction Method of Multipliers

High-resolution ultrasound (US) image reconstruction from a reduced number of measurements is of great interest in US imaging, since it could enhance both frame rate and image resolution. Compressive deconvolution (CD), combining compressed sensing and image deconvolution, represents an interesting possibility to consider this challenging task. The model of CD includes, in addition to the compressive sampling matrix, a 2-D convolution operator carrying the information on the system point spread function. Through this model, the resolution of reconstructed US images from compressed measurements mainly depends on three aspects: the acquisition setup, i.e., the incoherence of the sampling matrix, the image regularization, i.e., the sparsity prior, and the optimization technique. In this paper, we mainly focused on the last two aspects. We proposed a novel simultaneous direction method of multipliers based optimization scheme to invert the linear model, including two regularization terms expressing the sparsity of the RF images in a given basis and the generalized Gaussian statistical assumption on tissue reflectivity functions. The performance of the method is evaluated on both simulated and in vivo data.

Joint Segmentation and Deconvolution of Ultrasound Images Using a Hierarchical Bayesian Model Based on Generalized Gaussian Priors

This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images.

A blind deconvolution method for attenuative materials based on asymmetrical Gaussian model

During propagation in attenuative materials, ultrasonic waves are distorted by frequency-dependent acoustic attenuation. As a result, reference signals for blind deconvolution in attenuative materials are asymmetrical and should be accurately estimated by considering attenuation. In this study, an asymmetrical Gaussian model is established to estimate the reference signals from these materials, and a blind deconvolution method based on this model is proposed. Based on the symmetrical Gaussian model, the asymmetrical one is formulated by adding an asymmetrical coefficient. Upon establishing the model, the reference signal for blind deconvolution is determined via maximum likelihood estimation, and the blind deconvolution is implemented with an orthogonal matching pursuit algorithm. To verify the feasibility of the established model, spectra of ultrasonic signals from attenuative polyethylene plates with different thicknesses are measured and estimated. The proposed blind deconvolution method is applied to the A-scan signal and B-scan image from attenuative materials. Results demonstrate that the proposed method is capable of separating overlapping echoes and therefore achieves a high temporal resolution.

Blind Deconvolution of Ultrasound Images Using l1 -Norm-Constrained Block-Based Damped Variable Step-Size Multichannel LMS Algorithm

The problem of improving the ultrasound image resolution by undoing the effect of convolution on backscattered radio-frequency (RF) data caused by the point spread function (PSF) of ultrasonic imaging system is one of the key problems in the reconstruction of the medical ultrasound images. In this paper, the tissue reflectivity functions (TRFs) are directly estimated from the noisy and nonstationary RF data using the block-based multichannel least-mean square ( l1 -bMCLMS) algorithm without any prior knowledge of the PSF. To account for the nonstationarity and incomplete acquisition problem of the ultrasound RF data a modified block-based cross-relation equation has been developed. An l1 -norm regularized cost function based on the proposed modified cross-relation equation is then formulated for blind estimation of the TRFs using the new l1 -bMCLMS algorithm. A damped variable step-size is also developed to compensate for the noise effect and to improve the convergence speed of the algorithm. The PSF is then estimated from multiple lateral blocks of RF data using the regularized multiple-input/output inverse theorem, which is known to be suitable for both minimum and nonminimum phase signals. The salient feature of the proposed method is that no basis function is required for TRFs and/or PSF. The efficacy of the proposed method is examined using the simulation/experimental phantom data and in vivo RF data and evaluated in terms of the quality metrics: resolution gain (RG), normalized projection misalignment (NPM), and shifted normalized mean square error (snMSE). The results show that the RG and NPM improvements of TRFs estimation of 0.12 ∼ 5.2 and 3.34 ∼ 22.82 dB, respectively, and the snMSE improvement of the PSF estimation of the order 10(2 ∼ 4) can be achieved in our technique as compared with the other techniques in the literature.

Sparse deconvolution method for ultrasound images based on automatic estimation of reference signals

Sparse deconvolution is widely used in the field of non-destructive testing (NDT) for improving the temporal resolution. Generally, the reference signals involved in sparse deconvolution are measured from the reflection echoes of standard plane block, which cannot accurately describe the acoustic properties at different spatial positions. Therefore, the performance of sparse deconvolution will deteriorate, due to the deviations in reference signals. Meanwhile, it is inconvenient for automatic ultrasonic NDT using manual measurement of reference signals. To overcome these disadvantages, a modified sparse deconvolution based on automatic estimation of reference signals is proposed in this paper. By estimating the reference signals, the deviations would be alleviated and the accuracy of sparse deconvolution is therefore improved. Based on the automatic estimation of reference signals, regional sparse deconvolution is achievable by decomposing the whole B-scan image into small regions of interest (ROI), and the image dimensionality is significantly reduced. Since the computation time of proposed method has a power dependence on the signal length, the computation efficiency is therefore improved significantly with this strategy. The performance of proposed method is demonstrated using immersion measurement of scattering targets and steel block with side-drilled holes. The results verify that the proposed method is able to maintain the vertical resolution enhancement and noise-suppression capabilities in different scenarios.

Enhanced resolution pulse-echo imaging with stabilized pulses

Many pulse-echo imaging systems use focused beams to improve lateral resolution. The beam width is determined by the choice of source and apodization function, the frequency, and the physics of focusing. Postprocessing strategies to improve lateral resolution can be limited by the need for conditioning the mathematics of inverse filtering, due to instabilities. We present an analysis that defines key constraints on sampled versions of lateral beampatterns. Within these constraints are useful symmetric beampatterns, which, when properly sampled, can have a stable inverse filter. A framework for analysis and processing is described and applied to phantoms and tissues to demonstrate the improvements that can be realized.

Compressive Deconvolution in Medical Ultrasound Imaging

The interest of compressive sampling in ultrasound imaging has been recently extensively evaluated by several research teams. Following the different application setups, it has been shown that the RF data may be reconstructed from a small number of measurements and/or using a reduced number of ultrasound pulse emissions. Nevertheless, RF image spatial resolution, contrast and signal to noise ratio are affected by the limited bandwidth of the imaging transducer and the physical phenomenon related to US wave propagation. To overcome these limitations, several deconvolution-based image processing techniques have been proposed to enhance the ultrasound images. In this paper, we propose a novel framework, named compressive deconvolution, that reconstructs enhanced RF images from compressed measurements. Exploiting an unified formulation of the direct acquisition model, combining random projections and 2D convolution with a spatially invariant point spread function, the benefit of our approach is the joint data volume reduction and image quality improvement. The proposed optimization method, based on the Alternating Direction Method of Multipliers, is evaluated on both simulated and in vivo data.

In vivo deconvolution acoustic-resolution photoacoustic microscopy in three dimensions

Acoustic-resolution photoacoustic microscopy (ARPAM) provides a spatial resolution on the order of tens of micrometers, and is becoming an essential tool for imaging fine structures, such as the subcutaneous microvasculature. High lateral resolution of ARPAM is achieved using high numerical aperture (NA) of acoustic transducer; however, the depth of focus and working distance will be deteriorated correspondingly, thus sacrificing the imaging range and accessible depth. The axial resolution of ARPAM is limited by the transducer's bandwidth. In this work, we develop deconvolution ARPAM (D-ARPAM) in three dimensions that can improve the lateral resolution by 1.8 and 3.7 times and the axial resolution by 1.7 and 2.7 times, depending on the adopted criteria, using a 20-MHz focused transducer without physically increasing its NA and bandwidth. The resolution enhancement in three dimensions by D-ARPAM is also demonstrated by in vivo imaging of the microvasculature of a chick embryo. The proposed D-ARPAM has potential for biomedical imaging that simultaneously requires high spatial resolution, extended imaging range, and long accessible depth.

Point spread functions and deconvolution of ultrasonic images

This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

Broadband sparse-array blind deconvolution using frequency-difference beamforming

Synthetic time reversal (STR) is a technique for blind deconvolution of receiving-array recordings of sound from an unknown source in an unknown multipath environment. It relies on generic features of multipath sound propagation. In prior studies, the pivotal ingredient for STR, an estimate of the source-signal's phase (as a function of frequency ω), was generated from conventional beamforming of the received-signal Fourier transforms, P(j)(ω), 1 ≤ j ≤ N, where N is the number of array elements. This paper describes how STR is implemented even when the receiving-array elements are many wavelengths apart and conventional beamforming is inadequate. Here, the source-signal's phase is estimated by beamforming P(j)(*)(ω(1))P(j)(ω(2)) at the difference frequency ω(2) - ω(1). This extension of STR is tested with broadband signal pulses (11-19 kHz) and a vertical 16-element receiving array having a 3.75-m-spacing between elements using simple propagation simulations and measured results from the FAF06 experiment involving 2.2 km of down slope propagation from 46 to 92 m water depth. The cross-correlation coefficient between the source-broadcast and STR-reconstructed-signal waveforms for the simulations and experiments are 98% and 91%-92%, respectively. In addition, frequency-difference beamforming can be used to determine signal-path-arrival angles that conventional beamforming cannot.