Optimal apodization design for medical ultrasound using constrained least squares part I: theory

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

Volumn 54, Issue 2, 2007, Pages 332-341

  Guenther, Drake A ^b   Walker, William F ^a,b  

^a IEEE

^b University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMFORMING; BIOMEDICAL EQUIPMENT; IMAGE RESOLUTION; LEAST SQUARES APPROXIMATIONS; LINEAR ALGEBRA; MEDICAL IMAGING; OPTICAL TRANSFER FUNCTION; PRODUCT DESIGN; ULTRASONIC DEVICES;

APERTURE WEIGHTINGS; POINT RESOLUTION; QUADRATIC CONSTRAINTS; ULTRASOUND BEAMFORMER DESIGN;

ULTRASONIC IMAGING;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; COMPUTER AIDED DESIGN; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; ECHOGRAPHY; EQUIPMENT; EQUIPMENT DESIGN; EVALUATION; IMAGE ENHANCEMENT; INSTRUMENTATION; METHODOLOGY; QUALITY CONTROL; REGRESSION ANALYSIS; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ALGORITHMS; COMPUTER SIMULATION; COMPUTER-AIDED DESIGN; EQUIPMENT DESIGN; EQUIPMENT FAILURE ANALYSIS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; LEAST-SQUARES ANALYSIS; MODELS, BIOLOGICAL; QUALITY CONTROL; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; ULTRASONOGRAPHY;

EID: 33847750391     PISSN: 08853010     EISSN: None     Source Type: Journal    
DOI: 10.1109/TUFFC.2007.247     Document Type: Article

References (47)

1. C. L. Dolph, "A current distribution for broadside arrays which optimizes the relationship between beamwidth and sidelobe level," Proc. IRE, vol. 34, pp. 335-348, 1946.
2. T. T. Taylor, "Design of line source antennas for narrow beamwidth and low sidelobes," IRE Trans. Antennas Propagat., vol. AP-3, pp. 16-28, 1955.
3. A. T. Villeneuve, "'Taylor patterns for discrete arrays," IEEE Trans. Antennas Propagat., vol. 32, no. 10, pp. 1089-1093, 1984.
4. A. H. Nuttall, "Some windows with very good sidelobe behavior," IEEE Trans. Acoust. Speech Signal Processing, vol. 29, no. 1, pp. 84-91, 1981.
5. C. A. Olen and R. T. Compton, Jr., "A numerical pattern synthesis algorithm for arrays," IEEE Trans. Antennas Propagat., vol. 38, no. 10, pp. 1666-1676, 1990.
6. C.-Y. Tseng and L. J. Griffiths, "A simple algorithm to achieve desired patterns for arbitrary arrays," IEEE Trans. Signal Processing, vol. 40, no. 11, pp. 2737-2746, 1992.
7. I. W. Selesnick, M. Lang, and C. S. Burrus, "Constrained least square design of FIR filters without specified transition bands," IEEE Trans. Signal Processing, vol. 44, no. 8, pp. 1879-1892, 1996.
8. Y.-M. Law and C.-W. Kok, "Constrained eigenfilter design without specified transition bands," IEEE Trans. Circuits Syst. II: Express Briefs, vol. 52, no. 1, pp. 14-21, 2006.
9. S.-C. Pei and J.-J. Shyu, "2-D FIR eigenfilters: A least-squares approach," IEEE Trans. Circuits Syst., vol. 37, no. 1, pp. 24-43, 1990.
10. P. P. Vaidyanathan and T. Q. Nguyen, "Eigenfilters: A new approach to least-squares FIR filter design and applications including nyquist filters," IEEE Trans. Circuits Syst., vol. 34, no. 1, pp. 11-23, 1987.
11. M. H. Er, "Array pattern synthesis with a controlled mean-square sidelobe level," IEEE Trans. Signal Processing, vol. 40, no. 4, pp. 977-981, 1992.
12. S. L. Sim and M. H. Er, "Constrained optimization technique for general array pattern synthesis," Electron. Lett., vol. 32, no. 10, pp. 861-862, 1996.
13. M. H. Er, S. L. Sim, and S. N. Koh, "Application of constrained optimization techniques to array pattern synthesis," Signal Processing, vol. 34, pp. 323-334, 1993.
14. M. H. Er, "On the limiting solution of quadratically constrained broad-band beam formers," IEEE Trans. Signal Processing, vol. 41, no. 1, pp. 418-419, 1993.
15. S. L. Sim and M. H. Er, "Sidelobe suppression for general arrays in presence of element failures," Electron. Lett., vol. 33, no. 15, pp. 1278-1280, 1997.
16. B. P. Ng, M. H. Er, and C. Kot, "Linear array geometry synthesis with minimum sidelobe level and null control," IEE Proc. Microw. Antennas Propagat., vol. 141, no. 3, pp. 162-166, 1994.
17. E. S. Ebbini and C. Cain, "Multiple-focus ultrasound phased-array pattern synthesis: Optimal driving-signal distributions for hyperthermia," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 36, no. 5, pp. 540-548, 1989.
18. P.-C. Li, S. W. Flax, E. S. Ebbini, and M. O'Donnell, "Blocked element compensation in phased array imaging," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 40, no. 4, pp. 283-292, 1993.
19. B. Mandersson and G. Salomonsson, "Weighted least-squares pulse-shaping filters with application to ultrasonic signals," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 36, no. 1, pp. 109-113, 1989.
20. W. Wilkening, B. Brendel, H. Jiang, J. Lazenby, and H. Ermert, "Optimized receive filters and phase-coded pulse sequences for contrast agent and nonlinear imaging," in Proc. IEEE Ultrason. Symp., 2001, pp. 1733-1737.
21. W. Wilkening, B. Brendel, C. Hansen, and H. Ermert, "Optimized filters for dynamic RF echo blending in multiple focal zone imaging," in Proc. IEEE Ultrason. Symp., 2004, pp. 1729-1732.
22. K. Ranganathan and W. F. Walker, "A novel beamformer design method for medical ultrasound. Part I: Theory," IEEE Trans. Ultrason., Ferroelect, Freq. Contr., vol. 50, no. 1, pp. 15-24, 2003.
23. K. Ranganathan and W. F. Walker, "A novel beamformer design method for medical ultrasound. Part II: Results," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 50, no. 1, pp. 25-39, 2003.
24. S. Docolo and M. Moonen, "Design of far-field and near-field broadband beamformers using eigenfilters," Signal Processing, vol. 83, pp. 2641-2673, 2003.
25. O. Keitmann-Curdes, B. Brendel, C. Marg, and H. Ermert, "Optimization of apodization based on the sidelobe pressure energy in simulated ultrasound fields," in Proc. IEEE Ultrason. Symp., 2002, pp. 1677-1680.
26. R. Schwann, N. Stache, and T. G. Noll, "Optimization of frequency dependent receive apodization," in Proc. IEEE Ultrason. Symp., vol. 4, 2005, pp. 1988-1991.
27. M. D. Intriligator, Mathematical Optimization and Economic Theory. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2002, p. 258.
28. B. D. Steinberg, Principles of Aperture and Array System Design. New York: Wiley, 1976, pp. 40-52.
29. D. Vilkomerson, J. Greenleaf, and V. Dutt, "Towards a resolution metric for medical ultrasonic imaging," in Proc. IEEE Ultrason. Symp., 1995, pp. 1405-1410.
30. R. Johnson, "Contrast response analysis for medical ultrasound imaging," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, no. 4, pp. 805-809, 1997.
31. K. F. Üstüner and G. L. Holley, "Ultrasound imaging system performance assessment," presented at AAPM Annu. Meeting, 2003.
32. K. Ranganathan and W. F. Walker, "A general cystic resolution metric for medical ultrasound," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., submitted for publication.
33. D. A. Guenther and W. F. Walker, "Optimal apodization design for medical ultrasound using constrained least squares. Part II: Simulation results," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., this issue, pp. 000-000.
34. J. W. Goodman, Introduction to Fourier Optics. 3rd ed. Englewood, CO: Roberts & Company, 2005.
35. A. R. Selfridge, G. S. Kino, and B. T. Khuri-Yakub, "A theory for the radiation pattern of a narrow-strip acoustic transducer," Appl. Phys. Lett., vol. 37, no. 1, pp. 35-36, 1980.
36. S. W. Smith, R. F. Wagner, J. M. Sandrik, and H. Lopez, "Low contrast detectability and contrast/detail analysis in medical ultrasound," IEEE Trans. Sonics Ultrason., vol. 30, no. 3, pp. 164-173, 1983.
37. L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis. Reading, MA: Addison-Wesley, 1991.
38. Y. Y. Haimes, Risk Modeling, Assessment, and Management. 2nd ed. New York: Wiley, 2004.
39. G. H. Golub and C. F. Van Loan, Matrix Computations. 3rd ed. Baltimore: Johns Hopkins Univ. Press, 1996, pp. 375-378.
40. W. H. Gander, "Least squares with a quadratic constraint," Numerische Mathematik, vol. 36, pp. 291-307, 1981.
41. A. Björck, Numerical Methods for Least Squares Problems. Philadelphia: Society for Industrial and Applied Mathematics, 1996, pp. 203-213.
42. K. Thomenius, "Evolution of ultrasound beamformers," in Proc. IEEE Ultrason. Symp., 1996, pp. 1615-1622.
43. J. A. Jensen and P. Munk, "A new method for estimation of velocity vectors," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, pp. 837-851, 1998.
44. M. E. Anderson, "Spatial quadrature: A novel technique for multidimensional velocity estimation," in Proc. IEEE Ultrason. Symp., 1997, pp. 1233-1238.
45. W. F. Walker and G. E. Trahey, "A fundamental limit on delay estimation using partially correlated speckle signals," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 42, pp. 301-308, 1995.
46. S. W. Smith and H. Lopez, "A contrast-detail analysis of diagnostic ultrasound imaging," Med. Phys., vol. 9, no. 1, pp. 4-12, 1982.
47. C. K. Abbey, R. J. Zemp, J. Liu, K. K. Lindfors, and M. F. Insana, "Observer efficiency in discrimination tasks simulating malignant and benign breast lesions imaged with ultrasound," IEEE Trans. Med. Imag., vol. 25, no. 2, pp. 198-209, 2006.