|
|
|
| Clutter Removing Filter for Ultrasound Blood Flow Imaging Based on Low Rank Model |
| Du Yigang1,2, Zhang Mengyi3, Chen Siping1*, Li Yong2 |
1(National-Regional Key Technology Engineering Laboratory for MedicalUltrasound, Department of Biomedical Engineering, School of Medicine, Shenzhen University, Shenzhen 518060, Guangdong, China)
2(Shenzhen Mindray Bio-Medical Electronics Co. Ltd., Shenzhen 518057, Guangdong, China)
3(Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, China) |
|
|
|
|
Abstract The conventional ultrasound blood flow wall filter uses a fixed cut-off frequency, which is not effective when the tissue motion is different due to heart beat and breath. This paper presented an ultrasound clutter removing filter based on a low rank model. The characteristics of ultrasound flow signal was studied and formulated. The low rank model was comprised of a rank minimization and matrix sparsity problem. The convex optimization can be applied to solve it after relaxation. The novelty is that it is an adaptive filter due to the minimization of the combination of the nuclear norm and L1 norm. Ultrasound blood flow data were simulated. The filtered signals were obtained by three different orders FIR filters and the low rank filter. The RMS errors for FIR filtering were around 34%, 16% and 12% respectively, and lower than 0.001% when using the low rank filter, which not only improved the accuracy a lot but also maintained the same length of the filtered signal as the original one's, where the length of the FIR filtered signal was decreased compared to the original signal. However, the low rank model is much more complicated than the conventional method, and it is still difficult to be applied in a real-time ultrasound imaging system.
|
|
Received: 25 February 2016
|
|
|
|
|
|
[1] Jensen JA. Estimation of blood velocities using ultrasound: A signal processing approach[M]//New York: Cambridge University Press, 1996:19-22.
[2] Nicholas D. Evaluation of backscattering coefficients for excited human tissue: results, interpretation and associated measurements[J]. Ultrasound in Medicine and Biology, 1982, 8(1):17-28.
[3] Fei DY, Shung KK. Ultrasonic backscatter from mammalian tissues[J]. Journal of the Acoustical Society of America, 1985, 78:871-876.
[4] Yuan YW, Shung KK. Ultrasonic backscatter from flowing whole blood. II: dependence on shear frequency and fibrinogen concentration[J]. Journal of the Acoustical Society of America, 1988, 84:1195-1200.
[5] B?jrum S, Torp H, Kristoffersen K. Clutter filter design for ultrasound color flow imaging[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2002,49(2): 204-216.
[6] Jensen JA, Medical ultrasound imaging[J]. Progress in Biophysics and Molecular Biology, 2007,93: 153-165.
[7] Kasai C, Namekawa K, Koyano A, et al. Real-time two-dimensional blood flow imaging using an autocorrelation technique[J]. IEEE Transactions on Sonics and Ultrasonics, 1985, 32(3): 458-464.
[8] Udesen J, Gran F, Hansen KL, et al. High frame-rate blood vector velocity imaging using plane waves: simulations and preliminary experiments[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2008, 55(8):1729-1743.
[9] Jensen JA, Svendsen NB. Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1992, 39(2):262-267.
[10] Jensen JA. Field: A program for simulating ultrasound systems[J]. Medical and Biological Engineering and Computing, 1996, 34(Sup1-Part1):351-353.
[11] Jensen JA. Users’ guide for the Field II program[R]. Technical University of Denmark, Release 3.20, 2011.
[12] Hansen KL, Udesen J, Gran F, et al. Fast blood vector velocity imaging using ultrasound: in-vivo examples of complex blood flow in the vascular system[C]//Proceedings of IEEE International Ultrasonics Symposium. New York: IEEE, 2008:1068-1071.
[13] Leow CH, Bazigou E, Eckersley RJ, et al. Flow velocity mapping using contrast enhanced high-frame-rate plane wave ultrasound and image tracking: methods and initial in vitro and in vivo evaluation[J]. Ultrasound in Medicine and Biology, 2015, 41(11):2913-2925.
[14] Wright J, Ganesh A, Rao S, et al. Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization[C]//Advances in Neural Information Processing Systems. Red Hook: Curran Associates, 2009:2080-2088.
[15] Candes EJ, Wakin MB. An introduction to compressive sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2):21-30.
[16] Wright J, Yang AY, Ganesh A, et al. Robust face recognition via sparse representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2):210-227.
[17] Fazel M, Hindi H, Boyd SP. A rank minimization heuristic with application to minimum order system approximation[C]//Proceedings of IEEE American Control Conference. New York: IEEE, 2001, 6:4734-4739.
[18] Candes EJ, Recht B. Exact matrix completion via convex optimization[J]. Foundations of Computational mathematics,2009, 9(6):717-772.
[19] Candes EJ, Tao T. The power of convex relaxation: Near-optimal matrix completion[J]. IEEE Transactions on Information Theory, 2010, 56(5):2053-2080.
[20] Chandrasekaran V, Sanghavi S, Parrilo PA, et al. Rank sparsity incoherence for matrix decomposition[J]. SIAM Journal on Optimization, 2011, 21(2):572-596.
[21] Ledoux LA, Brands PJ, Hoeks AP. Reduction of the clutter component in Doppler ultrasound signals based on singular value decomposition: a simulation study[J]. Ultrasonic Imaging, 1997, 19:1-18.
[22] Tao Q, Wang Y, Fish P, et al. The wall signal removal in Doppler ultrasound systems based on recursive PCA[J].Ultrasound in Medicine and Biology, 2004, 30(3):369-379.
[23] Mauldin FW, Lin D, Hossack JA. A singular value filter for rejection of stationary artifact in medical ultrasound[C]//Proceedings of IEEE International Ultrasonics Symposium, New York: IEEE, 2010:359-362.
[24] Yu ACH, Cobbold R. Single-ensemble-based eigen-processing methods for color flow imaging-Part I. The Hankel-SVD filter[J].IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2008, 55(3):559-572.
[25] Yu ACH, Cobbold R. Single-ensemble-based eigen-processing methods for color flow imaging - Part II. The Matrix Pencil estimator[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2008, 55(3):573-587.
[26] Yu ACH, Lovstakken L. Eigen-based clutter filter design for ultrasound color flow imaging: a review[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2010, 57(5):1096-1111.
[27] Boyd S, Vandenberghe L. Convex Optimization[M] //New York: Cambridge University Press, 2004:168-169.
[28] Lin Z, Liu R, Su Z. Linearized alternating direction method with adaptive penalty for low rank representation[C] //Advances in Neural Information Processing Systems. Red Hook: Curran Associates, 2011:612-620.
[29] Lin Z, Chen M, Ma Y. The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices[R]. University of Illinois, UILU-ENG-09-2214, 2010. |
|
|
|
