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1.
Agarwal A  Yoo YM  Schneider FK  Kim Y 《Ultrasonics》2008,48(5):384-393
Quadrature demodulation-based phase rotation beamforming (QD-PRBF) is commonly used to support dynamic receive focusing in medical ultrasound systems. However, it is computationally demanding since it requires two demodulation filters for each receive channel. To reduce the computational requirements of QD-PRBF, we have previously developed two-stage demodulation (TSD), which reduces the number of lowpass filters by performing demodulation filtering on summation signals. However, it suffers from image quality degradation due to aliasing at lower beamforming frequencies. To improve the performance of TSD-PRBF with reduced number of beamforming points, we propose a new adaptive field-of-view (AFOV) imaging method. In AFOV imaging, the beamforming frequency is adjusted depending on displayed FOV size and the center frequency of received signals. To study its impact on image quality, simulation was conducted using Field II, phantom data were acquired from a commercial ultrasound machine, and the image quality was quantified using spatial (i.e., axial and lateral) and contrast resolution. The developed beamformer (i.e., TSD-AFOV-PRBF) with 1024 beamforming points provided comparable image resolution to QD-PRBF for typical FOV sizes (e.g., 4.6% and 1.3% degradation in contrast resolution for 160 mm and 112 mm, respectively for a 3.5 MHz transducer). Furthermore, it reduced the number of operations by 86.8% compared to QD-PRBF. These results indicate that the developed TSD-AFOV-PRBF can lower the computational requirement for receive beamforming without significant image quality degradation.  相似文献   

2.
Guenther DA  Walker WF 《Ultrasonics》2012,52(3):387-401
This paper proposes a novel receive beamformer architecture for broadband imaging systems that uses unique finite impulse response (FIR) filters on each channel. The conventional delay-and-sum (DAS) beamformer applies receive apodization by weighting the signal on each receive channel prior to beam summation. Our proposed FIR beamformer passes the focused receive radio frequency (RF) signals through multi-tap FIR filters on each receive channel prior to summation. The receive FIR filters are constructed to maximize the contrast resolution of the system’s spatial response. The broadband FIR beamformer produces spatial point spread functions (PSFs) with narrower mainlobe widths and lower sidelobe levels than spatial PSFs produced by the conventional DAS beamformer.We present simulation results showing that FIR filters of modest tap lengths (3-7) can yield marked improvement in image contrast and point resolution. Specifically we show that 7-tap FIR filters can reduce sidelobe and grating lobe energy by 30 dB and improve contrast resolution by as much as 20 dB compared to conventional apodization profiles. This improvement in contrast resolution comes at the expense of a decrease in beamformer sensitivity. We investigate the effects of phase aberration and show in simulation results that the multi-tap FIR beamformer outperforms the unaberrated DAS beamformer by 8-12 dB even in the presence of moderate aberration characterized by a root-mean-square strength of 28 ns and a full-width at half-maximum correlation length of 3.6 mm. We show experimental results wherein multi-tap FIR filters decrease sidelobe energy in the resulting 2D spatial response while achieving a narrow mainlobe. We also show results where the FIR beamformer improves the contrast to noise ratio (CNR) in simulated B-mode cyst images by more than 4 dB. Our algorithm has the potential to significantly improve ultrasound beamforming in any application where the system response is reasonably well characterized. Furthermore, this algorithm can be used to increase contrast and resolution in one-way beamforming systems such as acousto-optic and opto-acoustic imaging.  相似文献   

3.
The speed of sound in soft tissues is usually assumed to be 1540 m/s in medical pulse-echo ultrasound imaging systems. When the true speed is different, the mismatch can lead to distortions in the acquired images, and so reduce their clinical value. Previously we reported a new method of sound-speed estimation in the context of image deconvolution. Unlike most other sound-speed estimation methods, this enables the use of unmodified ultrasound machines and a normal scanning pattern. Our approach was validated for largely homogeneous media with single sound speeds. In this article, we demonstrate that sound speeds of dual-layered media can also be estimated through image deconvolution. An ultrasound simulator has been developed for layered media assuming that, for moderate speed differences, the reflection at the interface may be neglected. We have applied our dual-layer algorithm to simulations and in vitro phantoms. The speed of the top layer is estimated by our aforesaid method for homogeneous media. Then, when the layer boundary position is known, a series of deconvolutions are carried out with dual-layered point-spread functions having different lower-layer speeds. The best restoration is selected using a correlation metric. The error level (e.g., a mean error of −9 m/s with a standard deviation of 16 m/s) for in vitro phantoms is found to be not as good as that of our single-speed algorithm, but is comparable to other local speed estimation methods where the data acquisition may not be as simple as in our proposed method.  相似文献   

4.
Omari E  Lee H  Varghese T 《Ultrasonics》2011,51(6):758-767
Quantitative ultrasound features such as the attenuation slope, sound speed and scatterer size, have been utilized to evaluate pathological variations in soft tissues such as the liver and breast. However, the impact of variations in the sound speed and backscatter due to underlying fat content or fibrotic changes, on the attenuation slope has not been addressed. Both numerical and acoustically uniform tissue-mimicking experimental phantoms are used to demonstrate the impact of sound speed variations on attenuation slope using clinical real-time ultrasound scanners equipped with linear array transducers. Radiofrequency data at center frequencies of 4 and 5 MHz are acquired for the experimental and numerical phantoms respectively. Numerical phantom sound speeds between 1480 and 1600 m/s in increments of 20 m/s for attenuation coefficients of 0.3, 0.4, 0.5, 0.6, and 0.7 dB/cm/MHz are simulated. Variations in the attenuation slope when the backscatter intensity of the sample is equal, 3 dB higher, and 3 dB lower than the reference is also evaluated. The sound speed for the experimental tissue-mimicking phantoms were 1500, 1540, 1560 and 1580 m/s respectively, with an attenuation coefficient of 0.5 dB/cm/MHz. Radiofrequency data is processed using three different attenuation estimation algorithms, i.e. the reference phantom, centroid downshift, and a hybrid method. In both numerical and experimental phantoms our results indicate a bias in attenuation slope estimates when the reference phantom sound speed is higher (overestimation) or lower (underestimation) than that of the sample. This bias is introduced via a small spectral shift in the normalized power spectra of the reference and sample with different sound speeds. The hybrid method provides the best estimation performance, especially for sample attenuation coefficient values lower than that of the reference phantom. The performance of all the methods deteriorates when the attenuation coefficient of the reference phantom is lower than that of the sample. In addition, the hybrid method is the least sensitive to sample backscatter intensity variations.  相似文献   

5.
The results of a quantitative study of the impact of sound speed errors on the spatial resolution and amplitude sensitivity of a commercial medical ultrasound scanner are presented in the context of their clinical significance. The beamforming parameters of the scanner were manipulated to produce sound speed errors ranging over +/-8% while imaging a wire target and an attenuating, speckle-generating phantom. For the wire target, these errors produced increases in lateral beam width of up to 320% and reductions in peak echo amplitude of up to 10.5 dB. In the speckle-generating phantom, these errors produced increases in speckle intensity correlation cell area of up to 92% and reductions in mean speckle brightness of up to 5.6 dB. These results are applied in statistical analyses of two detection tasks of clinical relevance. The first is of low contrast lesion detectability, predicting the changes in the correct decision probability as a function of lesion size, contrast, and sound speed error. The second is of point target detectability, predicting the changes in the correct decision probability as function of point target reflectivity and sound speed error. Representative results of these analyses are presented and their implications for clinical imaging are discussed. In general, sound speed errors have a more significant impact on point target detectability over lesion detectability by these analyses, producing up to a 22% reduction in correct decisions for a typical error.  相似文献   

6.
Most of clinical ultrasound imaging systems use a pre-determined sound speed, mostly 1540 m/s, in transmit- and receive-beamforming while actual sound speed varies depending on tissue composition and temperature. Sound speed errors, particularly in receive-beamforming, lead to resolution degradation and sensitivity loss in ultrasound imaging. In this paper, we propose a sound speed estimation method in which an optimal sound speed, the speed that makes the echo signal delays at the transducer elements be best matched to the theoretical delays, is estimated by maximizing the beamformed echo signal amplitude with respect to the sound speed and the reflector displacement from the central axis of the ultrasound beam. Since the sound speed can be estimated from the echo signals on several scan lines, the proposed method does not require excessive computation. Experimental imaging studies of phantoms and porcine tissue with a 6 MHz 128-element linear probe and a 3 MHz 128-element convex probe have shown that spatial resolution, particularly in the lateral direction, can be improved by the proposed method.  相似文献   

7.
Radiofrequency ablation is the most common minimally invasive therapy used in the United States to treat hepatocellular carcinoma and liver metastases. The ability to perform real-time temperature imaging while a patient is undergoing ablation therapy may help reduce the high recurrence rates following ablation therapy. Ultrasound echo signals undergo time shifts with increasing temperature due to sound speed and thermal expansion, which are tracked using both 1D cross correlation and 2D block matching based speckle tracking methods. In this paper, we present a quantitative evaluation of the accuracy and precision of temperature estimation using the above algorithms on both simulated and experimental data.A finite element analysis simulation of radiofrequency ablation of hepatic tissue was developed. Finite element analysis provides a method to obtain the exact temperature distribution along with a mapping of the tissue displacement due to thermal expansion. These local displacement maps were combined with the displacement due to speed of sound changes and utilized to generate ultrasound radiofrequency frames at specified time increments over the entire ablation procedure. These echo signals provide an ideal test-bed to evaluate the performance of both speckle tracking methods, since the estimated temperature results can be compared directly to the exact finite element solution. Our results indicate that the 1D cross-correlation (CC) method underestimates the cumulative displacement by 0.20 mm, while the underestimation with 2D block matching (BM) is about 0.14 mm after 360 s of ablation. The 1D method also overestimates the size of the ablated region by 5.4% when compared to 2.4% with the 2D method after 720 s of ablation. Hence 2D block matching provides better tracking of temperature variations when compared to the 1D cross-correlation method over the entire duration of the ablation procedure. In addition, results obtained using 1D cross-correlation diverge from the ideal finite element results after 7 min of ablation and for temperatures greater than 65 °C.In a similar manner, experimental results presented using a tissue-mimicking phantom also demonstrate that the maximum percent difference with 2D block matching was 5%, when compared to 31% with the 1D method over the 700 s heating duration on the phantom.  相似文献   

8.
A constant sound speed of 1.54 mm/micros is generally used by ultrasound imaging systems for delay and timing. However, the body's sound speed in-homogeneity can lead to defocusing and increased clutter. To provide an improvement using standard transducers, the sound speed used in delay and timing was computed using different sound speeds. We observed improvement in lateral resolution and clutter in phantom, OB, abdominal, and breast imaging. In OB and abdominal imaging using a 4 MHz curved array, 1.48 mm/micros provided higher image quality in many situations. In breast with an 8 MHz linear array, 1.44 mm/micros provided better images in some cases. To provide an automated way to determine and adjust the sound speed used by the imaging system, an algorithm was developed that determines the sound speed that produces the best overall lateral image quality by analyzing the spatial frequency content in a single B-mode frame of channel data using images reconstructed using various trial sound speeds. The metric produced correlates well with the observed best lateral image quality.  相似文献   

9.
刘婷婷  周浩  郑音飞 《声学学报》2015,40(6):855-862
为了提高医学超声成像的空间分辨率,提出一种融合了特征空间最小方差与符号相干系数的波束形成方法。首先利用最小方差法计算回波数据的协方差矩阵和加权向量;然后对协方差矩阵进行特征分解得到信号子空间,并将加权向量投影到该空间上;最后计算符号相干系数,用于优化特征空间法得到的回波信号,最终获得超声成像数据。为验证算法的有效性,对医学超声成像中常用的点目标、斑目标进行仿真,对点目标仿体和人体颈动脉组织进行超声成像实验。结果表明:所提出的方法在分辨率、对比度以及稳健性等方面都优于传统的延时叠加算法、最小方差算法、特征空间最小方差法以及特征空间与相干系数融合的方法。   相似文献   

10.
Phase rotation beamforming (PRBF) is a commonly-used digital receive beamforming technique. However, due to its high computational requirement, it has traditionally been supported by hardwired architectures, e.g., application-specific integrated circuits (ASICs) or more recently field-programmable gate arrays (FPGAs). In this study, we investigated the feasibility of supporting software-based PRBF on a multi-core DSP. To alleviate the high computing requirement, the analog front-end (AFE) chips integrating quadrature demodulation in addition to analog-to-digital conversion were defined and used. With these new AFE chips, only delay alignment and phase rotation need to be performed by DSP, substantially reducing the computational load. We implemented the delay alignment and phase rotation modules on a Texas Instruments C6678 DSP with 8 cores. We found it takes 200 μs to beamform 2048 samples from 64 channels using 2 cores. With 4 cores, 20 million samples can be beamformed in one second. Therefore, ADC frequencies up to 40 MHz with 2:1 decimation in AFE chips or up to 20 MHz with no decimation can be supported as long as the ADC-to-DSP I/O requirement can be met. The remaining 4 cores can work on back-end processing tasks and applications, e.g., color Doppler or ultrasound elastography. One DSP being able to handle both beamforming and back-end processing could lead to low-power and low-cost ultrasound machines, benefiting ultrasound imaging in general, particularly portable ultrasound machines.  相似文献   

11.
Ultrasonic imaging is often used to estimate blood flow velocity. Currently, estimates are carried out using Doppler-based techniques. However, there are a number of shortcomings such as the limited spatial resolution and the inability to estimate longitudinal flows. Thus, alternative methods have been proposed to overcome them. Difficulties are notably encountered with high-frequency imaging systems that use swept-scan techniques. In this article, we propose to compare four vector velocity estimation methods that are complementary to Doppler, focusing on 40 MHz, high-frequency imaging. The goal of this study is to evaluate which method could circumvent the limitations of Doppler methods for evaluation of microcirculation, in the vessels having diameter on the order of 1 mm. We used two region-based approaches, one decorrelation-based approach and one spatiotemporal approach. Each method has been applied to seven flow sequences with various orientations and mean velocities. Four sequences were simulated with a system approach based on a 3D set of moving scatterers. Three experimental sequences were carried out by injecting blood-mimicking fluid within a gelatin phantom and then acquiring images with Visualsonics, Vevo 660 system. From velocity estimates, several performance criteria such as the normalized mean error or the normalized mean standard deviation were defined to compare the performance of the four estimators. The results show that region-based methods are the most accurate exhibiting mean errors less than 10% and mean standard deviation less than 13%. However, region-based approaches are those that require the highest calculative cost compared to the decorrelation-based method, which is the fastest. Finally, the spatiotemporal approach appeared to be a trade-off in terms of computational complexity and accuracy of estimates. It provides estimates with errors less than 10% for mean velocity and the CPU time is approximately 17 s for a ROI of size 40 * 80 pixels.  相似文献   

12.
刘兢本  郭良浩  董阁  闫超 《应用声学》2023,42(2):202-216
针对常规波束形成主瓣宽且目标分辨能力低的问题,提出一种基于深度卷积神经网络的波达方向估计方法。算法使用常规波束形成计算二维空间功率谱,将预处理后的空间功率谱图输入深度卷积神经网络。该文利用神经网络学习解卷积映射关系,输出主瓣宽度更窄的空间功率谱图,从而实现高分辨率二维波达方向估计。该算法对阵列结构没有限制,适用于立体阵。仿真结果表明该文方法在不同目标个数、快拍数及信噪比参数下均能准确估计目标方向。该文方法目标分辨能力优于常规波束形成方法。在低快拍情况下,目标方向估计误差低于自适应波束形成方法。  相似文献   

13.
Huang QH  Zheng YP  Lu MH  Chi ZR 《Ultrasonics》2005,43(3):153-163
3D ultrasound is a promising imaging modality for clinical diagnosis and treatment monitoring. Its cost is relatively low in comparison with CT and MRI, no intensive training and radiation protection is required for its operation, and its hardware is movable and can potentially be portable. In this study, we developed a portable freehand 3D ultrasound imaging system for the assessment of musculoskeletal body parts. A portable ultrasound scanner was used to obtain real-time B-mode ultrasound images of musculoskeletal tissues and an electromagnetic spatial sensor was fixed on the ultrasound probe to acquire the position and orientation of the images. The images were digitized with a video digitization device and displayed with its orientation and position synchronized in real-time with the data obtained by the spatial sensor. A program was developed for volume reconstruction, visualization, segmentation and measurement using Visual C++ and Visualization toolkits (VTK) software. A 2D Gaussian filter and a Median filter were implemented to improve the quality of the B-scan images collected by the portable ultrasound scanner. An improved distance-weighted grid-mapping algorithm was proposed for volume reconstruction. Temporal calibrations were conducted to correct the delay between the collections of images and spatial data. Spatial calibrations were performed using a cross-wire phantom. The system accuracy was validated by one cylinder and two cuboid phantoms made of silicone. The average errors for distance measurement in three orthogonal directions in comparison with micrometer measurement were 0.06 ± 0.39, −0.27 ± 0.27, and 0.33 ± 0.39 mm, respectively. The average error for volume measurement was −0.18% ± 5.44% for the three phantoms. The system has been successfully used to obtain the volume images of a fetus phantom, the fingers and forearms of human subjects. For a typical volume with 126 × 103 × 109 voxels, the 3D image could be reconstructed from 258 B-scans (640 × 480 pixels) within one minute using a portable PC with Pentium IV 2.4 GHz CPU and 512 MB memories. It is believed that such a portable volume imaging system will have many applications in the assessment of musculoskeletal tissues because of its easy accessibility.  相似文献   

14.
In medical ultrasound imaging field,in order to obtain high resolution and correct the phase errors induced by the velocity in-homogeneity of the tissue,a high-resolution medical ultrasound imaging method combining minimum variance beamforming and general coherence factor was presented.First,the data from the elements is delayed for focusing;then the multi-channel data is used for minimum variance beamforming;at the same time,the data is transformed from array space to beam space to calculate the general coherence factor;in the end, the general coherence factor is used to weight the results of minimum variance beamforming. The medical images are gotten by the imaging system.Experiments based on point object and anechoic cyst object are used to verify the proposed method.The results show the proposed method in the aspects of resolution,contrast and robustness is better than minimum variance beamforming and conventional beamforming.  相似文献   

15.
针对最小方差(MV)波束形成在算法稳健性和超声成像对比度方面存在的缺点,提出一种将特征空间法和前后向空间平滑法融合用于最小方差波束形成的超声成像方法。首先用前后向空间平滑取代传统的前向空间平滑,得到更精确的协方差矩阵;然后计算最优加权向量,并将该向量投影到由协方差矩阵特征空间构造的信号子空间中;最后利用投影所获得的向量与阵元数据进行运算得到成像回波数据。为了验证算法的有效性,对医学成像中常用的点目标和斑目标进行了成像实验。仿真结果表明:所提出的方法不依赖于对角加载参数的选取,在保持MV算法高分辨率的同时,还有效提高图像的对比度和算法的稳健性。   相似文献   

16.
It is desired that the same imaging functional modules such as beamformation, envelope detection, and digital scan conversion (DSC) are employed for the efficient development of a cross-sectional photoacoustic (PA) and ultrasound (US) dual-modality imaging system. The beamformation can be implemented using either delay-and-sum beamforming (DAS-BF) or adaptive beamforming methods, each with their own advantages and disadvantages for the dual-modality imaging. However, the DSC is always problematic because it causes blurring the fine details of an image, e.g., edges. This paper demonstrates that the pixel based focusing method is suitable for the dual-modality imaging; beamformation is directly conducted on each display pixel and thus DSC is not necessary. As a result, the artifacts by DSC are no longer a problem, so that the proposed method is capable of providing the maximum spatial resolution achievable by DAS-BF. The performance of the proposed method was evaluated through simulation and ex vivo experiments with a microcalcification-contained breast specimen, and the results were compared with those from DAS-BF and adaptive beamforming methods with DSC. The comparison demonstrated that the proposed method effectively overcomes the disadvantages of each beamforming method.  相似文献   

17.
Diffusion weighted magnetic resonance imaging (DWI) has been mostly acquired using single-shot echo-planar imaging (ss EPI) to minimize motion induced artifacts. The spatial resolution, however, is inherently limited in ss EPI especially for abdominal imaging, even with the advances in parallel imaging. A novel method of reduced Field of View ss EPI (rFOV ss EPI) has achieved high resolution DWI in human carotid artery, spinal cord with reduced blurring and higher spatial resolution than conventional ss EPI, but it has not been used to pancreas imaging. In the work, comparisons between the full FOV ss-DW EPI and rFOV ss-DW EPI in image qualities and ADC values of pancreatic tumors and normal pancreatic tissues were performed to demonstrate the feasibility of pancreatic high resolution rFOV DWI. There were no significant differences in the mean ADC values between full FOV DWI and rFOV DWI for the 17 subjects using b = 600 s/mm2 (P = 0.962). However, subjective scores of image quality was significantly higher at rFOV ss DWI (P = 0.008 and 0.000 for b-value = 0 s/mm2 and 600 s/mm2 respectively). The spatial resolution of DWI for pancreas was increased by a factor of over 2.0 (from almost 3.0 mm/pixel to 1.25 mm/pixel) using rFOV ss EPI technique. Reduced FOV ss EPI can provide good DW images and is promising to benefit applications for pancreatic diseases.  相似文献   

18.
When cutaneous fat layers are in the ultrasound imaging region, the phase aberration caused by the fat layers induce image distortion as well as spatial resolution degradation. The phase aberration may complicate clinical procedures particularly when ultrasound imaging is employed for spatial positioning of medical devices like a biopsy needle or HIFU. To compensate the fat layer effects more precisely in beamforming, an inclined-fat-layer model has been established from the magnetic resonance images of the same imaging region as in the ultrasound scanning. We have verified utility of the fat layer model by taking images of a metal needle put into an inclined-fat-layer mimicking phantom. The ultrasound images taken with a 128-element linear phase array operating at 6 MHz have shown better resolution and less distortion when receive beamforming was performed with the phase delay data derived from the inclined-fat-layer model.  相似文献   

19.
In this paper the total focusing method, the so called gold standard in classical beamforming, is compared with the widely used time-reversal MUSIC super resolution technique in terms of its ability to resolve closely spaced scatterers in a solid. The algorithms are tested with simulated and experimental array data, each containing different noise levels. The performance of the algorithms is evaluated in terms of lateral resolution and sensitivity to noise. It is shown that for the weak noise situation (SNR > 20 dB), time-reversal MUSIC provides significantly enhanced lateral resolution when compared to the total focusing method, breaking the diffraction limit. However, for higher noise levels, the total focusing method is shown to be robust, whilst the performance of time-reversal MUSIC is degraded. The influence of multiple scattering on the imaging algorithms is also investigated and shown to be small.  相似文献   

20.
I. Bazán  M. Vazquez  A. Vera 《Ultrasonics》2009,49(3):358-1606
Optimization of efficiency in hyperthermia requires a precise and non-invasive estimation of internal distribution of temperature. Although there are several research trends for ultrasonic temperature estimation, efficient equipments for its use in the clinical practice are not still available. The main objective of this work was to research about the limitations and potential improvements of previously reported signal processing options in order to identify research efforts to facilitate their future clinical use as a thermal estimator.In this document, we have a critical analysis of potential performance of previous ultrasonic research trends for temperature estimation inside materials, using different processing techniques proposed in frequency, time and phase domains. It was carried out in phantom with scatterers, assessing at their specific applicability, linearity and limitations in hyperthermia range. Three complementary evaluation indexes: technique robustness, Mat-lab processing time and temperature resolution, with specific application protocols, were defined and employed for a comparative quantification of the behavior of the techniques. The average increment per °C and mm was identified for each technique (3 KHz/°C in the frequency analysis, 0.02 rad/°C in the phase domain, while increments in the time domain of only 1.6 ns/°C were found). Their linearity with temperature rising was measured using linear and quadratic regressions and they were correlated with the obtained data.New improvements in time and frequency signal processing in order to reveal the potential thermal and spatial resolutions of these techniques are proposed and their subsequent improved estimation results are shown for simulated and measured A-scans registers. As an example of these processing novelties, an excellent potential resolution of 0.12 °C into hyperthermia range, with near-to-linear frequency dependence, could be achieved.Specifically defined “numerical” and physical multi-scatter phantoms are described, which mimic ultrasound velocity in tissues of about 1560 m/s @ 35 °C and have a quasi-uniform internal scattering structure designed to assure standard signal patterns adequate for processing comparisons in the same time and sound velocity conditions for all the techniques analyzed, and to obtain easily repeatable multi-pulse echo-patterns.A perfect lineal dependence (100% of correlation coefficient) between the unitary average increment measured by each technique and temperature rising was observed while working with simulated A-scan registers, where all the parameters are under an accurate control. Nevertheless a very small quadratic tendency appeared in the results obtained from experimental echo registers, which are more similar to a real tissues case. It would be an interesting future work to analyze the behavior of these techniques in real tissues in order to confirm or reject this light quadratic tendency.Finally, new methods were detailed and applied in order to precisely quantify the advantages of each estimation technique; their respective intrinsic limitations were also underlined.  相似文献   

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