Singular Value Decomposition Filtering Research Articles

Correlations between ultrafast power Doppler perfusion imaging variables and clinical disease activity in rheumatoid arthritis: potential applications for diagnosing and treating patients in deep clinical remission.

This study aimed to evaluate the ability of ultrafast power Doppler (PD) to assess disease activity in rheumatoid arthritis (RA) by examining the correlations between variables from ultrafast PD perfusion imaging and clinical measures of disease activity. Thirty-three RA patients underwent clinical assessments of disease activity and ultrasound scans of bilateral wrists using both ultrafast and conventional PD systems. A spatial singular value decomposition filter was applied to the ultrafast PD imaging. Singular vectors representing perfusion and fast flows were selected to produce perfusion images. All images were quantitatively analyzed with computer assistance and scored semiquantitatively (0-3) by a physician for synovial vascularity. The Pearson correlation coefficients between image variables and clinical indices were calculated. The correlation coefficients ranged from weakly to moderately positive between ultrafast PD variables and clinical indices (r=0.221-0.374, all P<0.05). The strongest correlations were observed for synovial PD brightness with the 28-joint Disease Activity Score based on C-Reactive Protein (DAS28-CRP) and the Simplified Disease Activity Index (SDAI). In patients within the deep clinical remission (dCR) subgroup, synovial PD brightness showed stronger correlations with DAS28-CRP, the Clinical Disease Activity Index, and SDAI (r=0.578-0.641, all P<0.001). The correlation coefficients between conventional PD variables and clinical indices were similar to those observed with ultrafast PD variables. Ultrafast PD imaging effectively extracts capillary blood signals and generates perfusion images. In the RA population, ultrafast PD variables exhibit weak-to-moderate correlations with clinical indices, with these correlations being notably stronger in dCR patients.

Reflection Artifacts Removal of Photoacoustic Imaging in Complex Medium

Abstract Photoacoustic (PA) imaging owns a great prospect in medical diagnosis because of its high contrast and capability in functional imaging. While, the detected PA signals are always a mix of direct-arrived signals (DAS) and reflected (scattered) signals (RS) in inhomogeneous and bounded samples such as human tissues. The RS can lead to many artifacts and severely affect the final image, which confuses the artifacts with the real PA sources. This paper employed a spatial singular value decomposition (SVD) filter to abstract the DAS and thus remove the reflection artifacts. We conducted experiments on an agar phantom and an in vitro tissue to verify the method. The results show that the proposed method can effectively remove RS, resulting in fewer reflection artifacts in PA images.

An adaptive spatiotemporal filter for ultrasound localization microscopy based on density canopy clustering

Ultrasound Localization Microscopy (ULM) facilitates structural and hemodynamic imaging of microvessels with a resolution of tens of micrometers. In ULM, the extraction of effective microbubble signals is crucial for image quality. Singular Value Decomposition (SVD) is currently the most prevalent method for microbubble signal extraction in ULM. Most existing ULM studies employ a fixed SVD filter threshold using empirical values which will lead to imaging quality degradation due to the insufficient separation of blood signals. In this study, we propose an adaptive and non-threshold SVD filter based on canopy-density clustering, termed DCC-SVD. This filter automatically classifies the components of the SVD based on the density of their spatiotemporal features, eliminating the need for parameter selection. In in vitro tube phantom, DCC-SVD demonstrated its ability to adaptive separation of blood and bubble signal at varying microbubble concentrations and flow rates. We compared the proposed DCC-SVD method with the Block-match 3D (BM3D) filter and a classical adaptive method called spatial similarity matrix (SSM), using concentration-variable in vivo rat brain data, as well as open-source rat kidney and mouse tumor datasets. The proposed DCC-SVD improved the global spatial resolution by approximately 4 μm from 30.39 μm to 26.02 μm. It also captured vessel structure absent in images obtained by other methods and yielded a smoother vessel intensity profile, making it a promising spatiotemporal filter for ULM imaging.

Dynamic Mode Decomposition for Transient Cavitation Bubbles Imaging in Pulsed High-Intensity Focused Ultrasound Therapy.

Pulsed high-intensity focused ultrasound (pHIFU) can induce sparse de novo inertial cavitation without the introduction of exogenous contrast agents, promoting mild mechanical disruption in targeted tissue. Because the bubbles are small and rapidly dissolve after each HIFU pulse, mapping transient bubbles and obtaining real-time quantitative metrics correlated with tissue damage are challenging. Prior work introduced Bubble Doppler, an ultrafast power Doppler imaging method as a sensitive means to map cavitation bubbles. The main limitation of that method was its reliance on conventional wall filters used in Doppler imaging and its optimization for imaging blood flow rather than transient scatterers. This study explores Bubble Doppler enhancement using dynamic mode decomposition (DMD) of a matrix created from a Doppler ensemble for mapping and extracting the characteristics of transient cavitation bubbles. DMD was first tested in silico with a numerical dataset mimicking the spatiotemporal characteristics of backscattered signal from tissue and bubbles. The performance of DMD filter was compared to other widely used Doppler wall filter-singular value decomposition (SVD) and infinite impulse response (IIR) high-pass filter. DMD was then applied to an ex vivo tissue dataset where each HIFU pulse was immediately followed by a plane wave Doppler ensemble. In silico DMD outperformed SVD and IIR high-pass filter and ex vivo provided physically interpretable images of the modes associated with bubbles and their corresponding temporal decay rates. These DMD modes can be trackable over the duration of pHIFU treatment using k-means clustering method, resulting in quantitative indicators of treatment progression.

Optimizing intracardiac flow assessment with high frequency ultrasound in a mouse model

Cardiomyopathy, a disorder affecting the heart muscle, is associated with severe symptoms, such as heart failure, arrhythmia, or cardiac arrest. Echocardiography is the primary clinical tool for myocardial assessment, which provides diagnostic and prognostic insights. However, current clinical parameters, such as myocardial strain, often detect the condition only after symptoms become pronounced, showing the need for early-stage assessment. Based on preliminary studies, intracardiac flow patterns have the potential to detect abnormal myocardial changes earlier than the current clinical parameters. Mouse models are commonly imaged with ultrasound in the cardiovascular disease research but their use for flow pattern evaluation has been hindered by spatial and temporal resolution limitations. Here, we address this limitation by conducting data acquisition using a Verasonics scanner with a range of high-frequency probes (16 to 42 MHz), transmit cycles, and transmit angles. A singular value decomposition (SVD) filter and frequency de-aliasing were also investigated to optimize flow quantification. Our findings show that a higher transmission frequency, while providing superior spatial resolution, may not yield the best flow quantification due to increased Doppler aliasing. Furthermore, SVD filtering and Doppler de-aliasing should be used with caution because improper implementation can adversely impact the quantification results.

Denoising four-dimensional flow magnetic resonance imaging data using a split-and-overlap approach via singular value decomposition

Four-dimensional flow magnetic resonance imaging (4D flow MRI) offers a powerful tool for visualizing fluid flows, critical for both diagnosing cardiovascular diseases and analyzing engineering fluid dynamics. Despite its potential in medical research, the clinical applicability of 4D flow MRI often faces challenges due to inherent noise. To mitigate this, we introduce the split-and-overlap singular value decomposition (SOSVD) filter, a distinctive noise reduction approach. Unlike traditional singular value decomposition methods, the SOSVD filter partitions the primary data matrix into overlapping subdomains and then applies singular value decomposition to each subdomain, preserving only the dominant mode for noise attenuation. Evaluations on simulated and experimental flow data within a square duct revealed a significant decrease in root mean square noise metrics. Moreover, when applied to in vivo aortic data, the SOSVD filter enhanced various flow determinants, including divergence, velocity gradients, streamlines, and velocity coherence. Thus, the SOSVD method presents a promising avenue for augmenting noise reduction in 4D flow MRI, potentially elevating diagnostic accuracy and enriching cardiovascular disease research.

Higher-order Singular Value Decomposition Filter for Contrast Echocardiography.

Assessing the coronary circulation with contrast-enhanced echocardiography has high clinical relevance. However, it is not being routinely performed in clinical practice because the current clinical tools generally could not provide adequate image quality. The contrast agent's visibility in the myocardium is generally poor, impaired by motion and non-linear propagation artifacts. The established multi-pulse contrast schemes (MPCS) and the more experimental singular value decomposition (SVD) filter also fall short to solve these issues. Here, we propose a scheme to process AM/AMPI echoes with higher-order singular value decomposition (HOSVD) instead of conventionally summing the complementary pulses. The echoes from the complementary pulses form a separate dimension in the HOSVD algorithm. Then, removing the ranks in that dimension with dominant coherent signals coming from tissue scattering would provide the contrast detection. We performed both in vitro and in vivo experiments to assess the performance of our proposed method in comparison with the current standard methods. A flow phantom study shows that HOSVD on AM pulsing exceeds the contrast-to-background ratio (CBR) of conventional AM and an SVD filter by 10dB and 14dB, respectively. In vivo porcine heart results also demonstrate that, compared to AM, HOSVD improves CBR in open-chest acquisition (up to 19dB) and contrast ratio in closed-chest acquisition (3dB).

Spatially segmented SVD clutter filtering in cardiac blood flow imaging with diverging waves

Ultrafast ultrasound imaging enables the visualization of rapidly changing blood flow dynamics in the chambers of the heart. Singular value decomposition (SVD) filters outperform conventional high pass clutter rejection filters for ultrafast blood flow imaging of small and shallow fields of view (e.g., functional imaging of brain activity). However, implementing SVD filters can be challenging in cardiac imaging due to the complex spatially and temporally varying tissue characteristics. To address this challenge, we describe a method that involves excluding the proximal portion of the image (near the chest wall) and divides the reduced field of view into overlapped segments, within which tissue signals are expected to be spatially and temporally coherent. SVD filtering with automatic selection of cut-off singular vector orders to remove tissue and noise signals is implemented for each segment. Auto-thresholding is based on the coherence of spatial singular vectors, delineating tissue, blood, and noise subspaces within a spatial similarity matrix calculated for each segment. Filtered blood flow signals from the segments are reconstructed and then combined and Doppler processing is used to form a set of blood flow images. Preliminary experimental results suggest that the spatially segmented approach improves the separation of the tissue and blood subsets in the spatial similarity matrix so that automatic thresholding is significantly improved, and tissue clutter can then be rejected more effectively in cardiac ultrafast imaging, compared to using the full field of view. In the case studied, spatially segmented SVD improved the rate of correct automatic selection of thresholds from 78% to 98.7% for the investigated cases and improved the post-filter power of blood signals by an average of more than 10 dB during a cardiac cycle.

A simulation framework for pulse wave and vector flow imaging using fluid–structure interaction and FIELD-II simulations

Pulse Wave Imaging (PWI) utilizes ultrasound elasticity imaging and normalized cross-correlation (NCC) tracking pulse-induced arterial wall distension propagations to perform localized pulse wave velocity and assess arterial compliance mapping for the early detection of vulnerable carotid plaques. At the same time, Vector Flow Imaging (VFI) using a singular value decomposition filter and NCC with axially and laterally shifted axial kernels provides blood flow information. In this study, fluid–structure interaction (FSI) simulations (FEBio) were integrated with FIELD-II ultrasound imaging simulations to optimize both PWI and VFI for simultaneous estimation of compliance and flow in structures of variable vessel geometry and plaque stiffness at distinct ultrasound parameters. The spatiotemporal maps of wall distension rate between FSI ground truth and PWI method were in excellent agreement (r2 = 0.968–0.982) at plane wave angles compounding at (−1°, 0, 1°) and NCC window size of 7 wavelengths in both straight and 87% stenotic vessel geometries. Similar agreement was found in 2D blood flow velocity estimation between FSI ground truth and VFI with a maximum correlation of 0.9464 at the systolic upstroke and r2 of 0.7426 at the angles of (−2°, 0, 2°) and NCC window size of 60 wavelengths. Overall, the framework presented herein allowed PWI and VFI technique validation and optimization prior to in vivo application.

Resolution and contrast improved ultrafast power Doppler microvessel imaging with null subtraction imaging

In this work, we demonstrate a novel non-linear beamforming technique, called null-subtraction imaging (NSI), to improve spatial resolution and image contrast of ultrafast, power Doppler microvessel imaging without significantly increasing computational cost compared to traditional delay and sum (DAS). NSI is a non-linear beamforming technique that operates on receive data by subtracting envelopes of beamforming results from three apodization windows. An array transducer and Verasonics Vantage 256 system were used to capture 1600 frames of raw ultrasonic radio frequency (RF) channel data by scanning a rat brain using nine plane waves spanning angles between -4° and 4° at a pulse repetition frequency of 1000 Hz. A singular value decomposition filter was applied on the raw RF channel data to filter out the tissue signal. Coherent compounding was performed individually on the beamformed result for each apodization window. Next, the subtraction of the envelopes for each apodization was conducted to form the NSI image. A total of 1,600 frames of NSI images were accumulated to form the final image. The NSI based ultrafast power Doppler microvessel imaging provided a ten-fold improvement in spatial resolution and a three-fold improvement in image contrast compared with the traditional DAS-based ultrafast power Doppler microvessel imaging.

Complex-domain SVD- and sparsity-based denoising for optical diffraction tomography

In this paper, we adopt a complex-domain cube filter (CCF) developed for hyperspectral 3D complex domain images for noise suppression of 3D complex-valued data in optical diffraction tomography. CCF is based on two processing steps: singular value decomposition (SVD) and complex-domain sparsity-based filter (CDID). SVD provides data compression and CDID noise suppression in the compressed domain. We demonstrate that the CCF algorithm can be used to denoise captured projections (sinogram), which results in enhanced tomographic reconstruction. The accuracy and quantitative advantage of CCF application are shown in simulation tests and in the processing of the experimental data. We show that the algorithm effectively suppresses noise and retrieves objects’ details even for highly noisy data.

Estimating the Neovascularity of Human Finger Tendon Through High-Frequency Ultrasound Micro-Doppler Imaging.

Neovascularization of injured tendons prolongs the proliferative phase of healing, but prolonged neovascularization may cause improper healing and pain. Currently, ultrasound Doppler imaging is used for measuring the neovascularization of injured tendons (e.g., Achilles tendon). However, the resolution of state-of-the-art clinical ultrasound machines is insufficient for visualizing the neovascularization in finger tendons. In this study, a high-frequency micro-Doppler imaging (HFμDI) based on 40-MHz ultrafast ultrasound imaging was proposed for visualizing the neovascularization in injured finger tendons during multiple rehabilitation phases. The vessel visibility was enhanced through a block-wise singular value decomposition filter and several curvilinear structure enhancement strategies, including the bowler-hat transform and Hessian-based vessel enhancement filtering. HFμDI was verified through small animal kidney and spleen imaging because the related vessel structure patterns of mice are well studied. Five patients with finger tendon injuries underwent HFμDI examination at various rehabilitation phases after surgery (weeks 11-56), and finger function evaluations were performed for comparisons. The results of small animal experiments revealed that the proposed HFμDI provides excellent microvasculature imaging performance; the contrast-to-noise ratio of HFμDI was approximately 15 dB higher than that of the conventional singular value decomposition filter, and the minimum detectable vessel size for mouse kidney was 35 μm without the use of contrast agent. In the human study, neovascularization was clearly observed in injured finger tendons during the early phase of healing (weeks 11-21), but it regressed from week 52 to 56. Finger rehabilitation appears to help reduce neovascularization; neovascular density decreased by approximately 1.8%-8.0% in participants after 4 weeks of rehabilitation. The experimental results verified the performance of HFμDI for microvasculature imaging and its potential for injured finger tendon evaluations.

Improving coronary ultrafast Doppler angiography using fractional moving blood volume and motion-adaptive ensemble length

Coronary microperfusion assessment is a key parameter for understanding cardiac function. Currently, coronary ultrafast Doppler angiography is the only non-invasive clinical imaging technique able to assess coronary microcirculation quantitatively in humans. In this study, we propose to use fractional moving blood volume (FMBV), proportional to the red blood cell concentration, as a metric for perfusion. FMBV compares the power Doppler in a region of interest (ROI) inside the myocardium to the power Doppler of a reference area in the heart chamber, fully filled with blood. This normalization gives then relative values of the ROI blood filling. However, due to the impact of ultrasound attenuation and elevation focus on power Doppler values, the reference area and the ROI need to be at the same depth to allow this normalization. This condition is rarely satisfied in vivo due to the cardiac anatomy. Hereby, we propose to locally compensate the attenuation between the ROI and the reference, by measuring the attenuation law on a phantom. We quantified the efficiency of this approach by comparing FMBV with and without compensation on a flow phantom. Compensated FMBV was able to estimate the ground-truth FMBV with less than 5% variation. This method was then adapted to the in vivo case of myocardial perfusion imaging during heart surgery on human neonates. The translation from in vitro to in vivo required an additional clutter filtering step to ensure that blood signals could be correctly identified in the fast-moving myocardium. We applied the singular value decomposition filter on temporal sliding windows whose lengths were a function of myocardium motion. This motion-adaptive temporal sliding window approach was able to improve blood and tissue separation in terms of contrast-to-noise ratio, as compared to well-established constant-length sliding window approaches. Therefore, compensated FMBV and singular value decomposition assisted with motion-adaptive temporal sliding windows improves the quantification of blood volume in coronary ultrafast Doppler angiography.

Overcoming camera instability problem for detecting and tracking moving objects in video using reduced data

Moving <span>objects detection is a vital field of study in various applications. Many of such applications may have to capture and process a lot of data, then such these data need to be reduced as much as possible in order to have a reasonable and suitable system for achieving the desired aims efficiently. The proposed algorithm utilizes singular value decomposition (SVD) and Bayer pattern filter for their good properties in producing very representative reduced data. This data is then handled by frame difference objects detection, which in turn is an approach that doesn’t need to handle much data. The camera shaking which can be caused by a windy weather in the case of the outdoor static camera may introduce a frame difference with imprecise moving objects detection, hence frames compensation is conducted utilizing a transformation based on speed up robust feature transform (SURF) detected key points.</span>

High-efficiency and precision VSP wavefield separation method via DCT

Abstract The processing efficiency of the widely used time-space (t-x) domain vertical seismic profiling (VSP) wavefield separation methods (such as median and singular value decomposition filtering) via one-dimensional discrete Fourier transform (DFT) depends on the wavefield separation method (or algorithm with processing parameter) and the total number of samples in the input VSP data. Once the wavefield separation method is determined, its processing efficiency is set and cannot be optimized. Although the popular frequency-wavenumber (f-k) domain VSP wavefield separation method via two-dimensional DFT has higher processing efficiency than the t-x domain VSP wavefield separation methods, its processing precision is susceptible to the spatial alias and Gibbs effects. For efficiency and precision improvements, we introduced the discrete cosine transform (DCT) operation into VSP wavefield separation for the first time, and proposed a high-efficiency and precision frequency-space (f-x) domain VSP wavefield separation method via DFT and DCT, in which the wavefield separation efficiency and precision can be optimized using the effective bandwidth cutoff frequency of the input VSP data. Based on the relationship between DFT and DCT, we combined their operations in the proposed method into one step (referred to as DCT–DFT) for further efficiency enhancement, thereby designing a high-efficiency and precision f-x domain VSP wavefield separation method via DCT–DFT. Theory analysis and synthetic and field VSP data examples show that the proposed method is highly efficient and precise, and can be widely used for three-dimensional (3D)-VSP data wavefield separation, especially for large distributed acoustic sensing (DAS)-VSP data.

Investigation on application of singular value decomposition filter in element domain for extraction of ultrasonic echoes from blood cells in jugular veins

The singular value decomposition (SVD) based clutter filter is commonly applied to beamformed signals for the visualization of echo signals from flowing blood cells. In this paper, the SVD-based clutter filter is applied to signals directly acquired from ultrasonic elements before beamforming to be compared with the conventional strategy by evaluating contrast and standard deviation (SD) in the filtered images. As a result, the contrast was improved from 10.7 ± 3.6 dB to 18.3 ± 4.6 dB, and the SD was slightly improved from 3.78 ± 0.69 dB to 3.07 ± 0.74 dB in the measurement of a right jugular vein.

Desempeño del método de Prony y del método del método del haz de matrices en la determinación de las frecuencias complejas naturales de resonancia de un sistema lineal

Characterization of a physical system is an important issue to approach some applied physics and engineering problems. The complex natural resonance frequencies of the system which are included in its impulsive response are characteristic of such system and are part of its description. Few works written in English language show a comparison among discrete methods that extract natural complex frequencies from a system impulsive response. Much less common is to find works written in Spanish language about this important research topic. Given this situation, important discrete numeric methods to estimate the complex natural resonance frequencies of a system through its impulsive response are described, tested and compared in different simulation scenarios in this document. According to the obtained results, the matrix pencil method with a SVD filter is the less sensitive method to the noise, while the Prony method and its different versions are the fastest ones. Scenarios that could be more suitable for each method are discussed.

High-Precision Iterative VSP Wavefield Separation

Conventional vertical seismic profiling (VSP) wavefield separation method (CSM) focuses on the wavefield separation result, not the residual. Usually, it cannot obtain desirable high-precision results. Iterative zero-offset VSP (ZVSP). However, IZSM only can be used for ZVSP data, which limits its application. The scalar wavefield separation algorithm used in IZSM is based on the SVD filtering, which limits its precision. The objective function threshold of IZSM is varied with the input ZVSP data, which limits its result precision and efficiency. To improve the wavefield separation precision and efficiency, we propose a high-precision iterative VSP wavefield separation method (HISM). HISM is suitable for both ZVSP and offset VSP (OVSP) data, and also applicable for any possible scalar wavefield separation algorithm The objective function threshold of HISM can be a fixed number. Therefore, HISM can obtain high precision and efficiency results. Actual ZVSP and OVSP data application demonstrates the performance of HISM.

Suppressing tissue clutter in the presence of motion and nonlinear propagation of ultrasound

Visualizing blood flow in small vessel with ultrasound imaging is a useful diagnosis tool for evaluating organ condition. The usage of encapsulated microbubbles that have non-linear response as contrast agents, in combination with pulsing schemes that suppress the linear tissue signal can improve the sensitivity and specificity of ultrasound flow imaging. However, the nonlinear propagation when ultrasound travels through tissue and microbubble clouds reduce contrast detection. Moreover, tissue motion causes clutter artifacts and imprecise combination of the multi-pulse transmission scheme, impairing image quality. We have previously developed an independent component analysis (ICA)-based clutter filter for high framerate imaging, which performed better than the widely used singular value decomposition (SVD) filter in presence of fast tissue motion. In this study, we examined the performance of ICA filter in combination with power modulation (PM) pulsing schemes to detect flow signal. We performed an in vitro- measurement that emulated ultrasound propagation through cloud of microbubbles and fast tissue motion. The results showed that the combination of PM and ICA filter achieved up to 6dB contrast-to-background ratio improvement compared to only PM. This improvement could be significant for myocardial perfusion imaging, where rapid tissue motion and nonlinear propagation through clouds of microbubbles are expected.

WEST tokamak hard x-ray tomography inversion

Long-pulse steady-state discharges with lower hybrid current drive were successfully obtained in the limiter configuration machine, Tore Supra. The hard x-ray (HXR) diagnostic system in Tore Supra associated with tomographic inversion provided a good approximation of the lower hybrid power deposition profile. The accurate plasma current control through this tomographic reconstruction leads to an improvement of plasma confinement. Tore Supra was upgraded to WEST, Tungsten (W) Environment in Steady-state Tokamak. The plasma geometry was changed to the D-shaped geometry. Therefore, a novel inversion code for WEST has been developed. The method used in the code is based on the Bessel function of the first kind of order zero. The code validation was performed using phantom emissivity profiles and WEST experimental data. It has been found that the line radiation of the tungsten divertor in WEST and noise significantly affect the inversion. The local HXR emissivity profile with acceptable accuracy can be achieved by applying a singular value decomposition filter and suppressing the lines of sight that intersect the divertors.