An algorithm for the de-noising of S-parameter data used in microwave imaging is proposed. The complex S-parameter frequency-sweep data are collected through scans over an acquisition surface and the algorithm separates efficiently the resulting two-dimensional responses (one frequency at a time) into a signal and a noise component. The separation is performed with an iterative procedure similar to the empirical mode decomposition. The signal component estimates the noise-free data, whereas the remaining data content estimates the noise and uncertainty in the measurement. The algorithm performance is verified with measured data.

References

1. 1)
  - 3. Dietrich, O., Raya, J.G., Reeder, S.B., et al: ‘Measurement of signal-to-noise ratios in MR images: influence of multichannel coils. Parallel imaging and reconstruction filters’, J. Magn. Reson. Imaging, 2007, 26, (2), pp. 375–385 (doi: 10.1002/jmri.20969).
2. 2)
  - 13. Tu, S., McCombe, J.J., Shumakov, D.S., et al: ‘Fast quantitative microwave imaging with point-spread function extracted from measurements’, Inverse Probl., 2015, 31, (045007), pp. 1–33.
3. 3)
  - 17. Sibson, R.: ‘A brief description of natural neighbor interpolation’, in Barnett, V. (Ed.): ‘Interpolating multivariate data’ (John Wiley & Sons, New York, NY, USA, 1981), ch. 2, pp. 21–36.
4. 4)
  - 14. Amineh, R.K., McCombe, J.J., Khalatpour, A., et al: ‘Microwave holography using measured point-spread functions’, IEEE Trans. Instrum. Meas., 2015, 64, (2), pp. 403–417 (doi: 10.1109/TIM.2014.2347652).
5. 5)
  - 12. Boudraa, A.O., Cexus, J.C., Saidi, Z.: ‘EMD-based signal noise reduction’, Int. J. Signal Process., 2004, 1, (1), pp. 33–37.
6. 6)
  - 22. Elshinawy, M.Y., Zeng, J., Lo, S.-C.B., et al: ‘Breast cancer detection in mammogram with AM–FM modeling and Gabor filtering’. Proc. Seventh Int. Conf. on Signal Processing (ICSP), Beijing, China, September 2004, vol. 3, pp. 2564–2567.
7. 7)
  - 4. McCombe, J.J., Nikolova, N.: ‘SNR assessment of microwave imaging systems’. Proc. IEEE AP-S/URSI Int. Symp. Antennas and Propagation, 2014, pp. 149–150.
8. 8)
  - 15. Box, G.E.P., Hunter, W.G., Hunter, J.S.: ‘Statistics for experimenters: an introduction to design, data analysis, and model building’ (John Wiley and Sons, Hoboken, NJ, USA, 1978).
9. 9)
  - 11. Boudraa, A.O., Cexus, J.C.: ‘EMD-based signal filtering’, IEEE Trans. Instrum. Meas., 2007, 56, (6), pp. 2196–2202 (doi: 10.1109/TIM.2007.907967).
10. 10)
  - 16. The MathWorks, MATLAB, Natick, MA, USA, 2015.
11. 11)
  - 9. Eyraud, C., Geffrin, J.-M., Litman, A., et al: ‘Drift correction for scattering measurements’, Appl. Phys. Lett., 2006, 89, (244104), pp. 1–3.
12. 12)
  - 17. Huang, N., Shen, Z., Long, S., et al: ‘The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis’, Proc. R. Soc. Lond. A, 1971, 454, pp. 903–995 (doi: 10.1098/rspa.1998.0193).
13. 13)
  - 12. Donoho, D.L.: ‘De-Noising by soft-thresholding’, IEEE Trans. Inf. Theory, 1995, 41, pp. 613–627 (doi: 10.1109/18.382009).
14. 14)
  - 5. Nikolova, N.K.: ‘Microwave biomedical imaging’ (Wiley Encyclopedia of Electrical and Electronics Engineering, 2014), pp. 1–22, (published online 25 April 2014), doi: 10.1002/047134608X.W8214.
15. 15)
  - 19. Liu, C., Wechsler, H.: ‘Gabor feature based classification using the enhanced fisher linear discriminant model for face recognition’, IEEE Trans. Image Process., 2002, 11, (4), pp. 467–476 (doi: 10.1109/TIP.2002.999679).
16. 16)
  - 1. Kaufman, L., Kramer, D.M., Crooks, L.E., et al: ‘Measuring signal-to-noise ratios in MR imaging’, Radiology, 1989, 173, (1), pp. 265–267 (doi: 10.1148/radiology.173.1.2781018).
17. 17)
  - 7. Proakis, J.G., Manolakis, D.G.: ‘Digital signal processing: principles, algorithms, and applications’ (Prentice-Hall, Englewood Cliffs, NJ, 1996, 3rd edn.).
18. 18)
  - 21. Pattichis, M.S., Bovik, A.C.: ‘Analyzing image structure by multidimensional frequency modulation’, IEEE Trans. Pattern Anal. Mach. Intell., 2007, 29, (5), pp. 753–766 (doi: 10.1109/TPAMI.2007.1051).
19. 19)
  - 20. Meshgini, S., Aghagolzadeh, A., Seyedarabi, H.: ‘Face recognition using Gabor-based direct linear discriminant analysis and support vector machine’, Comput. Electr. Eng., 2013, 39, (3), pp. 727–745 (doi: 10.1016/j.compeleceng.2012.12.011).
20. 20)
  - 2. Firbank, M.J., Coulthard, A., Harrison, R.M., et al: ‘A comparison of two methods for measuring the signal-to-noise ratio on MR images’, Phys. Med. Biol., 1999, 44, (12), pp. N261–N264 (doi: 10.1088/0031-9155/44/12/403).
21. 21)
  - 39. Lehmann, T.M., Gonner, C., Spitzer, K.: ‘Survey: interpolation methods in medical image processing’, IEEE Trans. Med. Imaging, 1999, 18, (11), pp. 1049–1075 (doi: 10.1109/42.816070).
22. 22)
  - 6. Eyraud, C., Litman, A., Herique, A., et al: ‘Microwave imaging from experimental data within a Bayesian framework with realistic random noise’, Inverse Probl., 2009, 25, (2), p. 024005 (doi: 10.1088/0266-5611/25/2/024005).

De-noising algorithm for enhancing microwave imaging

References

Related content