Complex principal components for robust motion estimation

[Comparison of wall filter algorithms for ultrasonic microvascular imaging]

The design of wall filter in ultrasonic microvascular imaging directly affects the resolution of blood flow imaging. We compared the traditional polynomial regression wall filter algorithm and two algorithms based on singular value decomposition (SVD), Full-SVD algorithm and RS-RSVD algorithm (random sampling based on random singular value decomposition) through experiments with simulated data and human renal entity data imaging experiments. The experimental results showed that the filtering effect of the traditional polynomial regression wall filter algorithm was limited, however, Full-SVD algorithm and RS-RSVD algorithm could better extract the micro blood flow signal from the tissue or noise signal. When RS-RSVD algorithm was randomly divided into 16 blocks, the signal-to-noise ratio was the same as that of Full-SVD algorithm, reduces the contrast-to-noise ratio by 2.05 dB, and reduces the execution time by 90.41%. RS-RSVD algorithm can improve the operation efficiency and is more conducive to the real-time imaging of high frame rate ultrasound microvessels.

Clutter suppression in ultrasound: performance evaluation and review of low-rank and sparse matrix decomposition methods

Vessel diseases are often accompanied by abnormalities related to vascular shape and size. Therefore, a clear visualization of vasculature is of high clinical significance. Ultrasound color flow imaging (CFI) is one of the prominent techniques for flow visualization. However, clutter signals originating from slow-moving tissue are one of the main obstacles to obtain a clear view of the vascular network. Enhancement of the vasculature by suppressing the clutters is a significant and irreplaceable step for many applications of ultrasound CFI. Currently, this task is often performed by singular value decomposition (SVD) of the data matrix. This approach exhibits two well-known limitations. First, the performance of SVD is sensitive to the proper manual selection of the ranks corresponding to clutter and blood subspaces. Second, SVD is prone to failure in the presence of large random noise in the dataset. A potential solution to these issues is using decomposition into low-rank and sparse matrices (DLSM) framework. SVD is one of the algorithms for solving the minimization problem under the DLSM framework. Many other algorithms under DLSM avoid full SVD and use approximated SVD or SVD-free ideas which may have better performance with higher robustness and less computing time. In practice, these models separate blood from clutter based on the assumption that steady clutter represents a low-rank structure and that the moving blood component is sparse. In this paper, we present a comprehensive review of ultrasound clutter suppression techniques and exploit the feasibility of low-rank and sparse decomposition schemes in ultrasound clutter suppression. We conduct this review study by adapting 106 DLSM algorithms and validating them against simulation, phantom, and in vivo rat datasets. Two conventional quality metrics, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), are used for performance evaluation. In addition, computation times required by different algorithms for generating clutter suppressed images are reported. Our extensive analysis shows that the DLSM framework can be successfully applied to ultrasound clutter suppression.

Deep Unfolded Robust PCA With Application to Clutter Suppression in Ultrasound

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A typical preprocessing step in super-resolution ultrasound is to separate the microbubble signal from the cluttering tissue signal. This step has a crucial impact on the final image quality. Here, we propose a new approach to clutter removal based on robust principle component analysis (PCA) and deep learning. We begin by modeling the acquired contrast enhanced ultrasound signal as a combination of low rank and sparse components. This model is used in robust PCA and was previously suggested in the context of ultrasound Doppler processing and dynamic magnetic resonance imaging. We then illustrate that an iterative algorithm based on this model exhibits improved separation of microbubble signal from the tissue signal over commonly practiced methods. Next, we apply the concept of deep unfolding to suggest a deep network architecture tailored to our clutter filtering problem which exhibits improved convergence speed and accuracy with respect to its iterative counterpart. We compare the performance of the suggested deep network on both simulations and in-vivo rat brain scans, with a commonly practiced deep-network architecture and with the fast iterative shrinkage algorithm. We show that our architecture exhibits better image quality and contrast.

Blind Source Separation-Based Motion Detector for Imaging Super-Paramagnetic Iron Oxide (SPIO) Particles in Magnetomotive Ultrasound Imaging

In magnetomotive ultrasound (MMUS) imaging, an oscillating external magnetic field displaces tissue loaded with super-paramagnetic iron oxide (SPIO) particles. The induced motion is on the nanometer scale, which makes its detection and its isolation from background motion challenging. Previously, a frequency and phase locking (FPL) algorithm was used to suppress background motion by subtracting magnetic field off ( -off) from on ( -on) data. Shortcomings to this approach include long tracking ensembles and the requirement for -off data. In this paper, a novel blind source separation-based FPL (BSS-FPL) algorithm is presented for detecting motion using a shorter ensemble length (EL) than FPL and without -off data. MMUS imaging of two phantoms containing an SPIO-laden cubical inclusion and one control phantom was performed using an open-air MMUS system. When background subtraction was used, contrast and contrast to noise ratio (CNR) were, respectively, 1.20±0.20 and 1.56±0.34 times higher in BSS-FPL as compared to FPL-derived images for EL < 3.5 s. However, contrast and CNR were similar for BSS-FPL and FPL for EL ≥ 3.5 s. When only -on data was used, contrast and CNR were 1.94 ± 0.21 and 1.56 ± 0.28 times higher, respectively, in BSS-FPL as compared to FPL-derived images for all ELs. Percent error in the estimated width and height was 39.30% ± 19.98% and 110.37% ± 6.5% for FPL and was 7.30% ± 7.6% and 16.21% ± 10.29% for BSS-FPL algorithm. This paper is an important step toward translating MMUS imaging to in vivo application, where long tracking ensembles would increase acquisition time and -off data may be misaligned with -on due to physiological motion.

Robust Short-Lag Spatial Coherence Imaging

Short-lag spatial coherence (SLSC) imaging displays the spatial coherence between backscattered ultrasound echoes instead of their signal amplitudes and is more robust to noise and clutter artifacts when compared with traditional delay-and-sum (DAS) B-mode imaging. However, SLSC imaging does not consider the content of images formed with different lags, and thus does not exploit the differences in tissue texture at each short-lag value. Our proposed method improves SLSC imaging by weighting the addition of lag values (i.e., M-weighting) and by applying robust principal component analysis (RPCA) to search for a low-dimensional subspace for projecting coherence images created with different lag values. The RPCA-based projections are considered to be denoised versions of the originals that are then weighted and added across lags to yield a final robust SLSC (R-SLSC) image. Our approach was tested on simulation, phantom, and in vivo liver data. Relative to DAS B-mode images, the mean contrast, signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) improvements with R-SLSC images are 21.22 dB, 2.54, and 2.36, respectively, when averaged over simulated, phantom, and in vivo data and over all lags considered, which corresponds to mean improvements of 96.4%, 121.2%, and 120.5%, respectively. When compared with SLSC images, the corresponding mean improvements with R-SLSC images were 7.38 dB, 1.52, and 1.30, respectively (i.e., mean improvements of 14.5%, 50.5%, and 43.2%, respectively). Results show great promise for smoothing out the tissue texture of SLSC images and enhancing anechoic or hypoechoic target visibility at higher lag values, which could be useful in clinical tasks such as breast cyst visualization, liver vessel tracking, and obese patient imaging.

Accelerated Singular Value-Based Ultrasound Blood Flow Clutter Filtering With Randomized Singular Value Decomposition and Randomized Spatial Downsampling

Singular value decomposition (SVD)-based ultrasound blood flow clutter filters have recently demonstrated substantial improvement in clutter rejection for ultrafast plane wave microvessel imaging, and have become the commonly used clutter filtering method for many novel ultrafast imaging applications such as functional ultrasound and super-resolution imaging. At present, however, the computational burden of SVD remains as a major hurdle for practical implementation and clinical translation of this method. To address this challenge, in the study we present two blood flow clutter filtering methods based on randomized SVD (rSVD) and randomized spatial downsampling to accelerate SVD clutter filtering with minimal compromise to the clutter filter performance. rSVD accelerates SVD computation by approximating the k largest singular values, while random downsampling accelerates both full SVD and rSVD by decomposing the original large data matrix into small matrices that can be processed in parallel. An in vitro blood flow phantom study with the presence of heavy tissue clutter showed significantly improved computational performance using the proposed methods with minimal deterioration to the clutter filter performance (less than 3-dB reduction in blood to clutter ratio, less than 0.2-cm²/s² increase in flow mean squared error, less than 0.1-cm/s increase in the standard deviation of the vessel blood flow signal, and less than 0.3-cm/s increase in tissue clutter velocity for both full SVD and rSVD when the downsampling factor was less than 20× ). The maximum acceleration was about threefold from randomized spatial downsampling, and approximately another threefold from rSVD. An in vivo rabbit kidney perfusion study showed that rSVD provided comparable performance to full SVD in clutter rejection in vivo (maximum difference of blood to clutter ratio was less than 0.6 dB), and random downsampling provided artifact-free perfusion imaging results when combined with both full SVD and rSVD. The blood to clutter ratio was still above 10 dB with a downsampling factor of 60× . We also demonstrated real-time microvessel imaging feasibility (~40-ms processing time) by combining rSVD with random downsampling. The findings and methods presented in this paper may greatly facilitate the new area of ultrafast microvessel imaging research.

A GPU-Parallelized Eigen-Based Clutter Filter Framework for Ultrasound Color Flow Imaging

Eigen-filters with attenuation response adapted to clutter statistics in color flow imaging (CFI) have shown improved flow detection sensitivity in the presence of tissue motion. Nevertheless, its practical adoption in clinical use is not straightforward due to the high computational cost for solving eigendecompositions. Here, we provide a pedagogical description of how a real-time computing framework for eigen-based clutter filtering can be developed through a single-instruction, multiple data (SIMD) computing approach that can be implemented on a graphical processing unit (GPU). Emphasis is placed on the single-ensemble-based eigen-filtering approach (Hankel singular value decomposition), since it is algorithmically compatible with GPU-based SIMD computing. The key algebraic principles and the corresponding SIMD algorithm are explained, and annotations on how such algorithm can be rationally implemented on the GPU are presented. Real-time efficacy of our framework was experimentally investigated on a single GPU device (GTX Titan X), and the computing throughput for varying scan depths and slow-time ensemble lengths was studied. Using our eigen-processing framework, real-time video-range throughput (24 frames/s) can be attained for CFI frames with full view in azimuth direction (128 scanlines), up to a scan depth of 5 cm ( λ pixel axial spacing) for slow-time ensemble length of 16 samples. The corresponding CFI image frames, with respect to the ones derived from non-adaptive polynomial regression clutter filtering, yielded enhanced flow detection sensitivity in vivo, as demonstrated in a carotid imaging case example. These findings indicate that the GPU-enabled eigen-based clutter filtering can improve CFI flow detection performance in real time.

Blind Source Separation - Based Motion Detector for Sub-Micrometer, Periodic Displacement in Ultrasonic Imaging

Sub-micrometer, periodic motion detection using blind source separation (BSS) via principal component analysis (PCA) is presented in the context of magnetomotive ultrasound (MMUS) imaging and Shearwave Dispersion Ultrasound Vibrometry (SDUV). In MMUS, an oscillating external magnetic field displaces tissue loaded with superparamagnetic iron oxide (SPIO) particles, whereas in SDUV, periodic tissue motion is induced using acoustic radiation force (ARF) to measure visco-elastic properties. BSS motion detection performance in MMUS imaging and SDUV was compared against frequency-phase locked (FPL) and normalized cross-correlation (NCC) motion detectors, respectively, in silico and in experimental phantoms. Parametric MMUS phantom images constructed using the BSS method had nearly twice the SNR of the corresponding images constructed using FPL method when a 0.043 mm or smaller kernel size was used. In FEM models of SDUV, the error in the BSS-estimated viscoelastic properties of simulated materials was < 10%, whereas the error was > 20% using NCC when the simulated SNR was 15 dB. In a calibrated elasticity phantom, the amplitude of the motion was ≤ 0.5 μm for a scanner power level ≤ 20%. The median percent error in BSS-derived shear modulus of the phantom was -6.8%, -1.55%, -17.11% for power level of 20%, 15%, and 10%, respectively. The corresponding NCC-derived errors were 29.90%, 127.1%, and 244.70%. These results suggest the relevance of using BSS for the detection of sub-micrometer, periodic motion in MMUS and SDUV imaging, particularly when SNR is less than 15 dB and/or induced displacements are less than 0.5 μm.

Improved Shear Wave Motion Detection Using Pulse-Inversion Harmonic Imaging With a Phased Array Transducer

Ultrasound tissue harmonic imaging is widely used to improve ultrasound B-mode imaging quality thanks to its effectiveness in suppressing imaging artifacts associated with ultrasound reverberation, phase aberration, and clutter noise. In ultrasound shear wave elastography (SWE), because the shear wave motion signal is extracted from the ultrasound signal, these noise sources can significantly deteriorate the shear wave motion tracking process and consequently result in noisy and biased shear wave motion detection. This situation is exacerbated in in vivo SWE applications such as heart, liver, and kidney. This paper, therefore, investigated the possibility of implementing harmonic imaging, specifically pulse-inversion harmonic imaging, in shear wave tracking, with the hypothesis that harmonic imaging can improve shear wave motion detection based on the same principles that apply to general harmonic B-mode imaging. We first designed an experiment with a gelatin phantom covered by an excised piece of pork belly and show that harmonic imaging can significantly improve shear wave motion detection by producing less underestimated shear wave motion and more consistent shear wave speed measurements than fundamental imaging. Then, a transthoracic heart experiment on a freshly sacrificed pig showed that harmonic imaging could robustly track the shear wave motion and give consistent shear wave speed measurements of the left ventricular myocardium while fundamental imaging could not. Finally, an in vivo transthoracic study of seven healthy volunteers showed that the proposed harmonic imaging tracking sequence could provide consistent estimates of the left ventricular myocardium stiffness in end-diastole with a general success rate of 80% and a success rate of 93.3% when excluding the subject with Body Mass Index higher than 25. These promising results indicate that pulse-inversion harmonic imaging can significantly improve shear wave motion tracking and thus potentially facilitate more robust assessment of tissue elasticity by SWE.

Experimental validation of displacement underestimation in ARFI ultrasound

Acoustic radiation force impulse (ARFI) imaging is an elastography technique that uses ultrasonic pulses to displace and track tissue motion. Previous modeling studies have shown that ARFI displacements are susceptible to underestimation due to lateral and elevational shearing that occurs within the tracking resolution cell. In this study, optical tracking was utilized to experimentally measure the displacement underestimation achieved by acoustic tracking using a clinical ultrasound system. Three optically translucent phantoms of varying stiffness were created, embedded with subwavelength diameter microspheres, and ARFI excitation pulses with F/1.5 or F/3 lateral focal configurations were transmitted from a standard linear array to induce phantom motion. Displacements were tracked using confocal optical and acoustic methods. As predicted by earlier finite element method studies, significant acoustic displacement underestimation was observed for both excitation focal configurations; the maximum underestimation error was 35% of the optically measured displacement for the F/1.5 excitation pulse in the softest phantom. Using higher F/#, less tightly focused beams in the lateral dimension improved accuracy of displacements by approximately 10 percentage points. This work experimentally demonstrates limitations of ARFI implemented on a clinical scanner using a standard linear array and sets up a framework for future displacement tracking validation studies.

Real-time targeted molecular imaging using singular value spectra properties to isolate the adherent microbubble signal

Ultrasound-based real-time molecular imaging in large blood vessels holds promise for early detection and diagnosis of various important and significant diseases, such as stroke, atherosclerosis, and cancer. Central to the success of this imaging technique is the isolation of ligand-receptor bound adherent microbubbles from free microbubbles and tissue structures. In this paper, we present a new approach, termed singular spectrum-based targeted molecular (SiSTM) imaging, which separates signal components using singular value spectra content over local regions of complex echo data. Simulations were performed to illustrate the effects of acoustic target motion and harmonic energy on SiSTM imaging-derived measurements of statistical dimensionality. In vitro flow phantom experiments were performed under physiologically realistic conditions (2.7 cm s⁻¹ flow velocity and 4 mm diameter) with targeted and non-targeted phantom channels. Both simulation and experimental results demonstrated that the relative motion and harmonic characteristics of adherent microbubbles (i.e. low motion and large harmonics) yields echo data with a dimensionality that is distinct from free microbubbles (i.e. large motion and large harmonics) and tissue (i.e. low motion and low harmonics). Experimental SiSTM images produced the expected trend of a greater adherent microbubble signal in targeted versus non-targeted microbubble experiments (P < 0.05, n = 4). The location of adherent microbubbles was qualitatively confirmed via optical imaging of the fluorescent DiI signal along the phantom channel walls after SiSTM imaging. In comparison with two frequency-based real-time molecular imaging strategies, SiSTM imaging provided significantly higher image contrast (P < 0.001, n = 4) and a larger area under the receiver operating characteristic curve (P < 0.05, n = 4).

Assessing and improving acoustic radiation force image quality using a 1.5-D transducer design

A 1.5-D transducer array was proposed to improve acoustic radiation force impulse (ARFI) imaging signal-to-noise ratio (SNRARFI) and image contrast relative to a conventional 1-D array. To predict performance gains from the proposed 1.5-D transducer array, an analytical model for SNRARFI upper bound was derived. The analytical model and 1.5-D ARFI array were validated using a finite element modelbased numerical simulation framework. The analytical model demonstrated good agreement with numerical results (correlation coefficient = 0.995), and simulated lesion images yielded a significant (2.92 dB; p < 0.001) improvement in contrast-tonoise ratio when rendered using the 1.5-D ARFI array.

The singular value filter: a general filter design strategy for PCA-based signal separation in medical ultrasound imaging

A general filtering method, called the singular value filter (SVF), is presented as a framework for principal component analysis (PCA) based filter design in medical ultrasound imaging. The SVF approach operates by projecting the original data onto a new set of bases determined from PCA using singular value decomposition (SVD). The shape of the SVF weighting function, which relates the singular value spectrum of the input data to the filtering coefficients assigned to each basis function, is designed in accordance with a signal model and statistical assumptions regarding the underlying source signals. In this paper, we applied SVF for the specific application of clutter artifact rejection in diagnostic ultrasound imaging. SVF was compared to a conventional PCA-based filtering technique, which we refer to as the blind source separation (BSS) method, as well as a simple frequency-based finite impulse response (FIR) filter used as a baseline for comparison. The performance of each filter was quantified in simulated lesion images as well as experimental cardiac ultrasound data. SVF was demonstrated in both simulation and experimental results, over a wide range of imaging conditions, to outperform the BSS and FIR filtering methods in terms of contrast-to-noise ratio (CNR) and motion tracking performance. In experimental mouse heart data, SVF provided excellent artifact suppression with an average CNR improvement of 1.8 dB with over 40% reduction in displacement tracking error. It was further demonstrated from simulation and experimental results that SVF provided superior clutter rejection, as reflected in larger CNR values, when filtering was achieved using complex pulse-echo received data and non-binary filter coefficients.

MR-guided thermotherapy of abdominal organs using a robust PCA-based motion descriptor

Thermotherapies can now be guided in real-time using magnetic resonance imaging (MRI). This technique is rapidly gaining importance in interventional therapies for abdominal organs such as liver and kidney. An accurate online estimation and characterization of organ displacement is mandatory to prevent misregistration and correct for motion related thermometry artifacts. In addition, when the ablation is performed with an extracorporal heating device such as high intensity focused ultrasound (HIFU), the continuous estimation of the organ displacement is the basis for the dynamic adjustment of the focal point position to track the targeted pathological tissue. In this paper, we describe the use of an optimized principal component analysis (PCA)-based motion descriptor to characterize in real-time the complex organ deformation during the therapy. The PCA was used to detect, in a preparative learning step, spatio-temporal coherences in the motion of the targeted organ. During hyperthermia, incoherent motion patterns could be discarded, which enabled improvements in motion estimation robustness, the compensation of motion related errors in thermal maps, and the adjustment of the beam position. The suggested method was evaluated for a moving phantom, and tested in vivo in the kidney and the liver of 12 healthy volunteers under free breathing conditions. The ability to perform a MR-guided thermotherapy in vivo during HIFU intervention was finally demonstrated on a porcine kidney.