AN ALTERNATIVE METHOD TO CLASSICAL ... - Semantic Scholar
AN ALTERNATIVE METHOD TO CLASSICAL BEAMFORMING FOR TRANSVERSE OSCILLATION IMAGES: APPLICATION TO ELASTOGRAPHY Franc¸ois Varray and Herv´e Liebgott Creatis, Universit´e de Lyon ; CNRS UMR 5220 ; INSERM U1044 ; INSA-Lyon ; Universit´e Lyon 1 [email protected] ABSTRACT Transverse oscillation techniques have shown their high potential for accurate and robust vector motion estimation for both flow and tissue. Unfortunately to form such images, it is necessary to modify the ultrasound scanner’s beamformer. This paper proposes alternative strategies to create transverse oscillation images in order to estimate motions in ultrasound images. The proposed methods are based on 1) one dimensional convolution or filtering of the radio frequency images or 2) two dimensional convolution or filtering of the B-mode images. They are first evaluated on a single lateral motion case in simulations and experiments, and then in a quasi-static elastography situation. The results with our filtering/convolution approach are very similar to the ones obtained with TO images obtained by classical beamforming. The mean deviation between the classical TO beamforming and the proposed method is 5.5%, which validates that one direction filtering is an efficient way to simplify the creation of TO images.
The problem of the so called TO images comes from the typical beamforming necessary to create the 2D oscillations. Indeed, a dynamic quadratic focussing and a specific apodization function are required to create the oscillations in both axial and lateral directions. Implementing this specific apodization requires to have access to the pre-beamformed signals which are the raw signals received by each active element of the probe before their summation into one radio-frequency (RF) line of the final US image. Even if in research scanners, these elementary signals are usually accessible, on commercial and clinical scanners only the B-mode images are usually available. In this paper, an alternative method is proposed to create TO images using either RF or B-mode images, in order to extend the number of scanners where motion estimation based on TO are possible. In the paper, the first part presents the TO classical beamforming and the proposed alternative methods. Then, results based on single lateral motion estimation and a quasistatic elastography measurements are proposed. A discussion closes the paper.
Index Terms— Transverse oscillation, motion estimation, elastography, ultrasound imaging 2. METHOD 1. INTRODUCTION To facilitate motion estimation in ultrasound (US) images, a specific beamforming has been developed to introduce a lateral oscillation in the US radio-frequency (RF) image. This technique, called transverse oscillations (TO), has been designed along with a specific phase-based motion estimator to estimate the displacement field in various applications [1]. The potentiality and interests of this technique has been shown in various applications such as in vector flow imaging [2], elastography imaging [3, 4] or echocardiography [5]. The 2D motion estimations obtained from TO images have shown to be more accurate and more robust than classical speckle tracking estimators. Efforts have also been conducted on the nonlinear propagation behaviour of the ultrasound in the medium with a multi-resolution estimation scheme [6]. Special thanks are due to Centre Lyonnais d’Acoustique (CeLyA), ANR grand n◦ 2011-LABX-014 for financial support.
2.1. Classical TO beamforming technique The classical TO beamforming is conducted on a receive only approach. The beamformer is designed according to the Fraunhofer approximation (FA) and a specific apodization featuring typically two peaks is used on the elementary RF signals received on each active element, wr . The apodization function is designed to produce an oscillation pattern in the lateral direction of the PSF: “ ”2 “ ” x+x0 2 0 1 −π x−x −π σ0 σ0 e +e (1) wr (x) = 2 where x is the element coordinate, 2x0 is the distance between the two Gaussian peaks and σ0 is their width at half maximum. In order to obtain a spatially unvarying PSF, the apodization function has to be adapted as a function of the propagation distance. The two parameters have to be defined
as a function of the axial distance z: ( x0 = λz/λx √ σ0 = 2λz/σx
(2)
where λ is the axial wavelength, λx and σx are the wavelength and the width at half maximum of the lateral profile of the PSF, respectively. Fig. 1.b represents a typical TO PSF obtained with this approach that shows oscillations in both axial and lateral directions. The shape of the PSF can be compared to the classical one (Fig. 1.a). 2.2. Alternative TO image formation technique As explained in the previous section, TO images are created on pre-beamformed signals, which are difficult to access on commercial clinical scanners. Here, an alternative solution is proposed to create this oscillatory pattern on RF or B-mode images. As show in Fig. 1.b, the objective is to obtain oscillations in the lateral direction, having a constant wavelength with the depth. Two main ideas are proposed, they consist in 1) convolution or 2) filtering. If RF images are used, the convolution/filtering is conducted only along the lateral direction. Indeed, the axial oscillations are already present in the RF signals. If B-mode images are used, the processing is conducted in both directions to create axial and lateral oscillations. In the lateral 1D convolution case, the objective is to create a kernel having an oscillatory pattern with a wavelength of λx . This kernel K(x) is defined as: K(x) = cos (2πx/λx ) H(x)
Values 245 µm 30 µm 6 mm 23 mm ∞
Table 1. LA523 probe parameters
can be estimated with this technique is half the wavelength of the axial or lateral PSF wavelength. In order to correctly estimate motion vectors larger than the mid-wavelength that can occur in many situations, the motion vectors estimated previously for the neighbour nodes are considered when estimating the displacement of a new node. This is an extremely efficient scheme for static elastography as the displacement close to the probe is very small and it increases as a function of depth. For this particular situation a triangular approach to cover the complete mesh is used as described in [7].
3. RESULTS The quantitative evaluation of the proposed solutions is done as follows. Two situations are studied: single lateral motion and quasi-static elastography. In all cases, the parameters for the TO are set with λx = 2.45 mm and σx = 7.35 mm.
(3)
where H(x) is a Hanning window which allows to smooth the border of the kernel. When the convolution is made in 2 directions on B-mode images, a similar kernel is used in both directions with: K(x, z) = cos (2πx/λx ) cos (2πz/λ) H(x)H(z)
Parameters Pitch Kerf Height Elevation focus Transmit focus
(4)
When filtering is used to create the TO images, a 5th -order band-pass Butterworth filter is used in the lateral direction. To create the correct oscillatory pattern, the bandpass filter BP is defined with: 1 1 1 1 − ; + (5) BP = λx σx λ x σx If B-mode images are used, the filtering is conducted in the axial direction using the transmitted signal frequency. The resulting images are proposed in Fig. 1. 2.3. Motion estimation The motion estimation is conducted with a previously developed motion estimator [1]. A regular grid is designed and the motion is estimated on each node. As the estimation is calculated based on phase information, the maximum value that
3.1. Single lateral motion In this section, a single lateral motion was applied to the imaged medium. A lateral displacement in the range [0; 0.7] mm was imposed to the medium. First, the CREANUIS simulator has been used to generate the images [8]. For each displacement, the initial scatterers position was translated and then, the new images were simulated. In the experimental measurements, a micro-metric table was used to impose an accurate displacement. The research platform ULA-OP [9] acquired the images. For both cases, the parameters of the LA523 probe (Esaote, Italy), summarized in Table 1, were used and the pre-beamformed signals were saved. A 5-cycle sinusoidal 5 MHz burst multiplied with a Gaussian window was transmitted in the medium. No apodization on the elements was used in transmission. The pre-beamformed signals were recorded for the classical TO beamforming. At the same time, the lateral convolution/filtering was conducted on the RF image. For 2D convolution/filtering, an envelope detection was first performed and 2D convolution/filtering was conducted on B-mode images. The resulting motion estimation are proposed in Fig. 2. The various approaches lead to equivalent results. The proposed techniques did not degrade the motion estimation compared to the classical TO image.
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 1. PSF obtained with (a) classical beamforming, (b) TO beamforming, (c) lateral convolution, (d) 2D convolution, (e) lateral filtering, and (f) 2D filtering. The PSF pattern are very similar.
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Fig. 2. Resulting motion estimation with the proposed techniques obtained (a) in simulation and (b) in experimental dataset. The mean value are slightly laterally moved to see the mean and standard deviation of the motion estimations.
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(c)
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(f)
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Fig. 3. Resulting motion (a-e) and strain (f-j) images obtained with the classical TO beamforming and the proposed approaches. 3.2. Experimental elastography To evaluate the proposed TO techniques on more complex experimental dataset, an elastography phantom was used (Phan-
tom Model 049, CIRS Inc., Norfolk, VA). The same excitation signal as in the previous situation was used. In quasistatic elastography, a manual compression is applied by the
Convolution 5.5%
2D convolution 14.7%
Filtering 6.6%
2D filtering 16.2%
Table 2. Mean deviation compare to the classical TO beamforming with the proposed methods. user using the probe in order to create a displacement and deform the structures inside the medium. Then, the motion is estimated in both axial and lateral directions. Then, strain images are computed by derivation of the motion in axial or lateral direction. To evaluate the similarity between the proposed strategies and the classical one, the mean deviation of the stain images are computed: M DX = |S X − S T O |
(6)
where ◦ is the mean value of the pixel-to-pixel difference between the strain images based on classical TO and the X proposed technique. The resulting images are proposed in Fig. 3 only for the axial motion. Indeed, in this experimental situation, the lateral displacement is weak and not useful for the methods estimation. Exception made when working on Bmode images, the resulting estimation of the motion are very close to the elastography images of the classical TO beamforming. The obtained mean deviations, proposed in Table 2, also translate such behaviour. It also seems better to use RF images. 4. DISCUSSION AND CONCLUSION In this paper, two different strategies have been proposed to generate TO images. Indeed, classical beamforming requires the access to pre-beamformed signals, which are difficult to obtain. With convolution/filtering in one or two directions, TO images are created from RF or B-mode images. A quantitative evaluation of the proposed approaches has been conducted in two situations. First, using lateral displacement of the medium in simulations and experiments. No method overcomes the others and they are comparable to the classical TO beamforming. Then, in quasi-static experiments, the obtained elastography images are similar to the reference TO beamforming one, exception made of the 2D convolution and 2D filtering. This demonstrates the potential of an alternative strategies to create TO images even if deeper efforts have to be continue to work on B-mode imaging. The proposed methodology opens new perspectives for motion estimation. Indeed, the access to B-mode images is easy on ultrasound scanner. The TO image beamforming can be conducted after the initial beamforming of the scanner on the RF, B-mode or TGC images. The implementation is direct and easier compared to classical TO beamforming. With an efficient motion estimator implementation, the TO images beamformed and exploited on commercial and clinical equipments. Moreover, GPU programming can be done both for
the beamforming and the motion estimator. Also, by filtering the B-mode images, the frequencies used, both in axial and lateral directions, can be arbitrarily chosen. In this way, the multi-resolution scheme, proposed our previous work [6], can be tested with a large range of frequencies in both directions and are no more limited by the hardware equipments. 5. REFERENCES [1] A. Basarab, H. Liebgott, and P. Delachartre, “Analytic estimation of subsample spatial shift using the phases of multidimensional analytic signals,” IEEE Transactions on Image Processing, vol. 18, no. 2, pp. 440–447, 2009. [2] J.A. Jensen and Peter Munk, “A new method for estimation of velocity vectors,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 45, pp. 837–851, 1998. [3] H. Liebgott, J. Fromageau, J.E. Wilhjelm, D. Vray, and P. Delachartre, “Beamforming scheme for 2d displacement estimation in ultrasound imaging,” Eurasip J Appl Signal Process, vol. 8, pp. 1212–1220, 2005. [4] C. Sumi, “Displacement vector measurement using instantaneous ultrasound signal phase-multidimensional autocorrelation and doppler methods,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 55, no. 1, pp. 24–43, 2008. [5] H. Liebgott, A. Ben Salem, A. Basarab, H. Gao, P. Claus, J. D’hooge, P. Delachartre, and D. Friboulet, “Tangential sound field oscillations for 2d motion estimation in echocardiography,” in IEEE International Ultrasonics Symposium, 2009, pp. 498–501. [6] F. Varray and H. Liebgott, “Multi resolution transverse oscillations for movement estimation in ultrasound images,” in IEEE International Symposium on Biomedical Imaging, 2012, pp. 1120–1123. [7] A. Basarab, P. Gueth, H. Liebgott, and P. Delachartre, “Phase-based block matching applied to motion estimation with unconventional beamforming strategies,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 56, no. 5, pp. 945–957, 2009. [8] F. Varray, C. Cachard, P. Tortoli, and O. Basset, “Nonlinear radio frequency image simulation for harmonic imaging - CREANUIS,” in IEEE International Ultrasonics Symposium, 2010, pp. 2179–2182. [9] P. Tortoli, L. Bassi, E. Boni, A. Dallai, F. Guidi, and S. Ricci, “ULA-OP: an advanced open platform for ultrasound research,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 56, no. 10, pp. 2207–2216, 2009.
The problem of the so called TO images comes from the typical beamforming necessary to create the 2D oscillations. Indeed, a dynamic quadratic focussing and a specific apodization function are required to create the oscillations in both axial and lateral directions. Implementing this specific apodization requires to have access to the pre-beamformed signals which are the raw signals received by each active element of the probe before their summation into one radio-frequency (RF) line of the final US image. Even if in research scanners, these elementary signals are usually accessible, on commercial and clinical scanners only the B-mode images are usually available. In this paper, an alternative method is proposed to create TO images using either RF or B-mode images, in order to extend the number of scanners where motion estimation based on TO are possible. In the paper, the first part presents the TO classical beamforming and the proposed alternative methods. Then, results based on single lateral motion estimation and a quasistatic elastography measurements are proposed. A discussion closes the paper.
Index Terms— Transverse oscillation, motion estimation, elastography, ultrasound imaging 2. METHOD 1. INTRODUCTION To facilitate motion estimation in ultrasound (US) images, a specific beamforming has been developed to introduce a lateral oscillation in the US radio-frequency (RF) image. This technique, called transverse oscillations (TO), has been designed along with a specific phase-based motion estimator to estimate the displacement field in various applications [1]. The potentiality and interests of this technique has been shown in various applications such as in vector flow imaging [2], elastography imaging [3, 4] or echocardiography [5]. The 2D motion estimations obtained from TO images have shown to be more accurate and more robust than classical speckle tracking estimators. Efforts have also been conducted on the nonlinear propagation behaviour of the ultrasound in the medium with a multi-resolution estimation scheme [6]. Special thanks are due to Centre Lyonnais d’Acoustique (CeLyA), ANR grand n◦ 2011-LABX-014 for financial support.
2.1. Classical TO beamforming technique The classical TO beamforming is conducted on a receive only approach. The beamformer is designed according to the Fraunhofer approximation (FA) and a specific apodization featuring typically two peaks is used on the elementary RF signals received on each active element, wr . The apodization function is designed to produce an oscillation pattern in the lateral direction of the PSF: “ ”2 “ ” x+x0 2 0 1 −π x−x −π σ0 σ0 e +e (1) wr (x) = 2 where x is the element coordinate, 2x0 is the distance between the two Gaussian peaks and σ0 is their width at half maximum. In order to obtain a spatially unvarying PSF, the apodization function has to be adapted as a function of the propagation distance. The two parameters have to be defined
as a function of the axial distance z: ( x0 = λz/λx √ σ0 = 2λz/σx
(2)
where λ is the axial wavelength, λx and σx are the wavelength and the width at half maximum of the lateral profile of the PSF, respectively. Fig. 1.b represents a typical TO PSF obtained with this approach that shows oscillations in both axial and lateral directions. The shape of the PSF can be compared to the classical one (Fig. 1.a). 2.2. Alternative TO image formation technique As explained in the previous section, TO images are created on pre-beamformed signals, which are difficult to access on commercial clinical scanners. Here, an alternative solution is proposed to create this oscillatory pattern on RF or B-mode images. As show in Fig. 1.b, the objective is to obtain oscillations in the lateral direction, having a constant wavelength with the depth. Two main ideas are proposed, they consist in 1) convolution or 2) filtering. If RF images are used, the convolution/filtering is conducted only along the lateral direction. Indeed, the axial oscillations are already present in the RF signals. If B-mode images are used, the processing is conducted in both directions to create axial and lateral oscillations. In the lateral 1D convolution case, the objective is to create a kernel having an oscillatory pattern with a wavelength of λx . This kernel K(x) is defined as: K(x) = cos (2πx/λx ) H(x)
Values 245 µm 30 µm 6 mm 23 mm ∞
Table 1. LA523 probe parameters
can be estimated with this technique is half the wavelength of the axial or lateral PSF wavelength. In order to correctly estimate motion vectors larger than the mid-wavelength that can occur in many situations, the motion vectors estimated previously for the neighbour nodes are considered when estimating the displacement of a new node. This is an extremely efficient scheme for static elastography as the displacement close to the probe is very small and it increases as a function of depth. For this particular situation a triangular approach to cover the complete mesh is used as described in [7].
3. RESULTS The quantitative evaluation of the proposed solutions is done as follows. Two situations are studied: single lateral motion and quasi-static elastography. In all cases, the parameters for the TO are set with λx = 2.45 mm and σx = 7.35 mm.
(3)
where H(x) is a Hanning window which allows to smooth the border of the kernel. When the convolution is made in 2 directions on B-mode images, a similar kernel is used in both directions with: K(x, z) = cos (2πx/λx ) cos (2πz/λ) H(x)H(z)
Parameters Pitch Kerf Height Elevation focus Transmit focus
(4)
When filtering is used to create the TO images, a 5th -order band-pass Butterworth filter is used in the lateral direction. To create the correct oscillatory pattern, the bandpass filter BP is defined with: 1 1 1 1 − ; + (5) BP = λx σx λ x σx If B-mode images are used, the filtering is conducted in the axial direction using the transmitted signal frequency. The resulting images are proposed in Fig. 1. 2.3. Motion estimation The motion estimation is conducted with a previously developed motion estimator [1]. A regular grid is designed and the motion is estimated on each node. As the estimation is calculated based on phase information, the maximum value that
3.1. Single lateral motion In this section, a single lateral motion was applied to the imaged medium. A lateral displacement in the range [0; 0.7] mm was imposed to the medium. First, the CREANUIS simulator has been used to generate the images [8]. For each displacement, the initial scatterers position was translated and then, the new images were simulated. In the experimental measurements, a micro-metric table was used to impose an accurate displacement. The research platform ULA-OP [9] acquired the images. For both cases, the parameters of the LA523 probe (Esaote, Italy), summarized in Table 1, were used and the pre-beamformed signals were saved. A 5-cycle sinusoidal 5 MHz burst multiplied with a Gaussian window was transmitted in the medium. No apodization on the elements was used in transmission. The pre-beamformed signals were recorded for the classical TO beamforming. At the same time, the lateral convolution/filtering was conducted on the RF image. For 2D convolution/filtering, an envelope detection was first performed and 2D convolution/filtering was conducted on B-mode images. The resulting motion estimation are proposed in Fig. 2. The various approaches lead to equivalent results. The proposed techniques did not degrade the motion estimation compared to the classical TO image.
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(b)
(c)
(d)
(e)
(f)
Fig. 1. PSF obtained with (a) classical beamforming, (b) TO beamforming, (c) lateral convolution, (d) 2D convolution, (e) lateral filtering, and (f) 2D filtering. The PSF pattern are very similar.
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(b)
Fig. 2. Resulting motion estimation with the proposed techniques obtained (a) in simulation and (b) in experimental dataset. The mean value are slightly laterally moved to see the mean and standard deviation of the motion estimations.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
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Fig. 3. Resulting motion (a-e) and strain (f-j) images obtained with the classical TO beamforming and the proposed approaches. 3.2. Experimental elastography To evaluate the proposed TO techniques on more complex experimental dataset, an elastography phantom was used (Phan-
tom Model 049, CIRS Inc., Norfolk, VA). The same excitation signal as in the previous situation was used. In quasistatic elastography, a manual compression is applied by the
Convolution 5.5%
2D convolution 14.7%
Filtering 6.6%
2D filtering 16.2%
Table 2. Mean deviation compare to the classical TO beamforming with the proposed methods. user using the probe in order to create a displacement and deform the structures inside the medium. Then, the motion is estimated in both axial and lateral directions. Then, strain images are computed by derivation of the motion in axial or lateral direction. To evaluate the similarity between the proposed strategies and the classical one, the mean deviation of the stain images are computed: M DX = |S X − S T O |
(6)
where ◦ is the mean value of the pixel-to-pixel difference between the strain images based on classical TO and the X proposed technique. The resulting images are proposed in Fig. 3 only for the axial motion. Indeed, in this experimental situation, the lateral displacement is weak and not useful for the methods estimation. Exception made when working on Bmode images, the resulting estimation of the motion are very close to the elastography images of the classical TO beamforming. The obtained mean deviations, proposed in Table 2, also translate such behaviour. It also seems better to use RF images. 4. DISCUSSION AND CONCLUSION In this paper, two different strategies have been proposed to generate TO images. Indeed, classical beamforming requires the access to pre-beamformed signals, which are difficult to obtain. With convolution/filtering in one or two directions, TO images are created from RF or B-mode images. A quantitative evaluation of the proposed approaches has been conducted in two situations. First, using lateral displacement of the medium in simulations and experiments. No method overcomes the others and they are comparable to the classical TO beamforming. Then, in quasi-static experiments, the obtained elastography images are similar to the reference TO beamforming one, exception made of the 2D convolution and 2D filtering. This demonstrates the potential of an alternative strategies to create TO images even if deeper efforts have to be continue to work on B-mode imaging. The proposed methodology opens new perspectives for motion estimation. Indeed, the access to B-mode images is easy on ultrasound scanner. The TO image beamforming can be conducted after the initial beamforming of the scanner on the RF, B-mode or TGC images. The implementation is direct and easier compared to classical TO beamforming. With an efficient motion estimator implementation, the TO images beamformed and exploited on commercial and clinical equipments. Moreover, GPU programming can be done both for
the beamforming and the motion estimator. Also, by filtering the B-mode images, the frequencies used, both in axial and lateral directions, can be arbitrarily chosen. In this way, the multi-resolution scheme, proposed our previous work [6], can be tested with a large range of frequencies in both directions and are no more limited by the hardware equipments. 5. REFERENCES [1] A. Basarab, H. Liebgott, and P. Delachartre, “Analytic estimation of subsample spatial shift using the phases of multidimensional analytic signals,” IEEE Transactions on Image Processing, vol. 18, no. 2, pp. 440–447, 2009. [2] J.A. Jensen and Peter Munk, “A new method for estimation of velocity vectors,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 45, pp. 837–851, 1998. [3] H. Liebgott, J. Fromageau, J.E. Wilhjelm, D. Vray, and P. Delachartre, “Beamforming scheme for 2d displacement estimation in ultrasound imaging,” Eurasip J Appl Signal Process, vol. 8, pp. 1212–1220, 2005. [4] C. Sumi, “Displacement vector measurement using instantaneous ultrasound signal phase-multidimensional autocorrelation and doppler methods,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 55, no. 1, pp. 24–43, 2008. [5] H. Liebgott, A. Ben Salem, A. Basarab, H. Gao, P. Claus, J. D’hooge, P. Delachartre, and D. Friboulet, “Tangential sound field oscillations for 2d motion estimation in echocardiography,” in IEEE International Ultrasonics Symposium, 2009, pp. 498–501. [6] F. Varray and H. Liebgott, “Multi resolution transverse oscillations for movement estimation in ultrasound images,” in IEEE International Symposium on Biomedical Imaging, 2012, pp. 1120–1123. [7] A. Basarab, P. Gueth, H. Liebgott, and P. Delachartre, “Phase-based block matching applied to motion estimation with unconventional beamforming strategies,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 56, no. 5, pp. 945–957, 2009. [8] F. Varray, C. Cachard, P. Tortoli, and O. Basset, “Nonlinear radio frequency image simulation for harmonic imaging - CREANUIS,” in IEEE International Ultrasonics Symposium, 2010, pp. 2179–2182. [9] P. Tortoli, L. Bassi, E. Boni, A. Dallai, F. Guidi, and S. Ricci, “ULA-OP: an advanced open platform for ultrasound research,” IEEE Trans Ultrason Ferroelectr Freq Control, vol. 56, no. 10, pp. 2207–2216, 2009.
