Two-dimensional blind Bayesian deconvolution of medical ultrasound images

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.

Computation of Photoacoustic Absorber Size from Deconvolved Photoacoustic Signal Using Estimated System Impulse Response

Photoacoustic signal recorded by photoacoustic imaging system can be modeled as convolution of initial photoacoustic response by the photoacoustic absorber with the system impulse response. Our goal was to compute the size of photoacoustic absorber using the initial photoacoustic response, deconvolved from the recorded photoacoustic data. For deconvolution, we proposed to use the impulse response of the photoacoustic system, estimated using discrete wavelet transform based homomorphic filtering. The proposed method was implemented on experimentally acquired photoacoustic data generated by different phantoms and also verified by a simulation study involving photoacoustic targets, identical to the phantoms in experimental study. The photoacoustic system impulse response, which was estimated using the acquired photoacoustic signal corresponding to a lead pencil, was used to extract initial photoacoustic response corresponding to a mustard seed of 0.65 mm radius. The recovered radius values of the mustard seed, corresponding to the experimental and simulation studies were 0.6 mm and 0.7 mm.

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.

Observing Bubble Cavitation by Back-Propagation of Acoustic Emission Signals

Temporal- and spatial-resolved observations of microbubble cavitation generated through high-intensity ultrasound irradiation are key in improving both the efficiency and efficacy of ultrasound-assisted drug delivery systems. A method of measuring bubble cavitation applying an image-reconstruction technique of back-propagation of an acoustic cavitation emission (ACE) signal is proposed. A high-intensity focused ultrasound wave (pump wave) irradiates the bubble synchronously using ultrasound recording equipment to acquire the timing of the RF signal, which is produced when the bubble radiates a secondary wave during bubble cavitation. The ACE signal source is reconstructed through ultrasound-wave back-propagation followed by amplitude deconvolution. The proposed method was applied to microbubbles of an ultrasound contrast agent by changing the sound pressure of the pump wave. The method reliability of the temporal resolution was verified by simulating the amplitude-modulated signal of the virtual sound source. The temporal transition of the ACE signal exhibited sub-microsecond-order fluctuations in the signal intensity. From the amplitude signal image and the instantaneous frequency image reconstruction of the proposed method, two different ACE phenomena were visualized. One is the periodic pattern by the beat signals from the harmonic and ultraharmonic component of nonlinear oscillation under low-intensity ultrasound conditions. The other is the nonperiodic temporal and spatial distributions of this irradiation under high-intensity ultrasound conditions.

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.

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.

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.

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.

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.

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.

A simulation study on the choice of regularization parameter in ℓ2-norm ultrasound image restoration

Ultrasound image deconvolution has been widely investigated in the literature. Among the existing approaches, the most common are based on ℓ2-norm regularization (or Tikhonov optimization) or the well-known Wiener filtering. However, the success of the Wiener filter in practical situations largely depends on the choice of the regularization hyperparameter. An appropriate choice is necessary to guarantee the balance between data fidelity and smoothness of the deconvolution result. In this paper, we revisit different approaches for automatically choosing this regularization parameter and compare them in the context of ultrasound image deconvolution via Wiener filtering. Two synthetic ultrasound images are used in order to compare the performances of the addressed methods.

Contrast-ultrasound dispersion imaging for prostate cancer localization by improved spatiotemporal similarity analysis

Angiogenesis plays a major role in prostate cancer growth. Despite extensive research on blood perfusion imaging aimed at angiogenesis detection, the diagnosis of prostate cancer still requires systematic biopsies. This may be due to the complex relationship between angiogenesis and microvascular perfusion. Analysis of ultrasound-contrast-agent dispersion kinetics, determined by multipath trajectories in the microcirculation, may provide better characterization of the microvascular architecture. We propose the physical rationale for dispersion estimation by an existing spatiotemporal similarity analysis. After an intravenous ultrasound-contrast-agent bolus injection, dispersion is estimated by coherence analysis among time-intensity curves measured at neighbor pixels. The accuracy of the method is increased by time-domain windowing and anisotropic spatial filtering for speckle regularization. The results in 12 patient data sets indicated superior agreement with histology (receiver operating characteristic curve area = 0.88) compared with those obtained by reported perfusion and dispersion analyses, providing a valuable contribution to prostate cancer localization.

A blind deconvolution approach to ultrasound imaging

In this paper, a single-input multiple-output (SIMO) channel model is introduced for the deconvolution process of ultrasound imaging; the ultrasound pulse is the single system input and tissue reflectivity functions are the channel impulse responses. A sparse regularized blind deconvolution model is developed by projecting the tissue reflectivity functions onto the null space of a cross-relation matrix and projecting the ultrasound pulse onto a low-resolution space. In this way, the computational load is greatly reduced and the estimation accuracy can be improved because the proposed deconvolution model contains fewer variables. Subsequently, an alternating direction method of multipliers (ADMM) algorithm is introduced to efficiently solve the proposed blind deconvolution problem. Finally, the performance of the proposed blind deconvolution method is examined using both computer-simulated data and practical in vitro and in vivo data. The results show a great improvement in the quality of ultrasound images in terms of signal-to-noise ratio and spatial resolution gain.

Robust finite impulse response beamforming applied to medical ultrasound

We previously described a beamformer architecture that replaces the single apodization weights on each receive channel with channel-unique finite impulse response (FIR) filters. The filter weights are designed to optimize the contrast resolution performance of the imaging system. Although the FIR beamformer offers significant gains in contrast resolution, the beamformer suffers from low sensitivity, and its performance rapidly degrades in the presence of noise. In this paper, a new method is presented to improve the robustness of the FIR beamformer to electronic noise as well as variation or uncertainty in the array response. A method is also described that controls the sidelobe levels of the FIR beamformer's spatial response by applying an arbitrary weighting function in the filter design algorithm. The robust FIR beamformer is analyzed using a generalized cystic resolution metric that quantifies a beamformer's clinical imaging performance as a function of cyst size and channel input SNR. Fundamental performance limits are compared between 2 robust FIR beamformers - the dynamic focus FIR (DF-FIR) beamformer and the group focus FIR (GF-FIR) beamformer - the conventional delay-and-sum (DAS) beamformer, and the spatial-matched filter (SMF) beamformer. Results from this study show that the new DF- and GF-FIR beamformers are more robust to electronic noise compared with the optimal contrast resolution FIR beamformer. Furthermore, the added robustness comes with only a slight loss in cystic resolution. Results from the generalized cystic resolution metric show that a 9-tap robust FIR beamformer outperforms the SMF and DAS beamformer until receive channel input SNR drops below -5 dB, whereas the 9-tap optimal contrast resolution beamformer's performance deteriorates around 50 dB SNR. The effects of moderate phase aberrations, characterized by an a priori root-mean-square strength of 28 ns and an a priori full-width at half-maximum correlation length of 3.6 mm, are investigate- d on the robust FIR beamformers. Full sets of robust FIR beamformer filter weights are constructed using an in silico model scanner and the L14-5/38 mm probe. Using the derived weights, a series of simulated point target and anechoic cyst B-mode images are generated to investigate further the potential increases in contrast resolution when using the robust FIR beamformers. Under the investigated conditions, the 7-tap optimal contrast resolution beamformer and the 7-tap robust beamformer with added SNR constraint increase lesion detectability by 247 and 137% compared with the conventional DAS beamformer, respectively. Finally, experimental phantom and in vivo images are produced using this novel receive architecture. The simulated and experimental images clearly show a reduction in clutter and an increase in contrast resolution compared with the conventionally beamformed images. This novel receive beamformer can be applied to any conventional ultrasound system where the system response is reasonably well characterized.