1. DETECTION OF BREAST CANCER WITH A NEW FACTORIZATION APPROACH

2. INTRODUCTION Why we use microwave: 1. X-ray is main method a. But it causes ionization b. It has high false negative rates(%4-%34) 2. MRI is another solution a. Its resolution is high b. But over diagnosis rate is high c. Also its cost is high 3. Ultrasound has a false negative rate of %17(See [1]) Conclusion: Microwave can be a better solution in terms of cost, health risks and detection rate.

3. INTRODUCTION What we have done in this work: 1. We adapt new factorization approach, given in [2], to our problem. 2. Then we try to solve problem in three different configurations(Given in next slight) 3. We also proposed a new numerical approach to decrease computational complexity of direct problem.

4. INTRODUCTION Free space (Or space filled with just one material) Half space with lower half space filled with perfect electric conductor (PEC) Two layered media

5. MOTIVATION OF DIRECT AND INVERSE PROBLEMS

7. In general it is very hard to evaluate such integrals, but to reduce computational complexity, we used some approaches. 1) Parellel algorithms 2) Using FFT to calculate inverse Fourier transform

8. MOTIVATION OF DIRECT AND INVERSE PROBLEMS For FFT our works are continuing, but we achive to give some examples. The best side is algorithm complexity reduces  But it requires different techniques to solve: 1) Stability problems 2) Reduction of number of samples etc.

9. MOTIVATION OF DIRECT AND INVERSE PROBLEMS Here we used the new factorization method in [2]. This is different from traditional factorization method proposed in [3]. In [3]  Basis is Green functions In [2]  Basis is, so it is fast

10. MOTIVATION OF DIRECT AND INVERSE PROBLEMS

11. NUMERICAL RESULTS Breast model used is taken from real MRI data. It was a 3D model but we use some slices of it. 313*213 points -> 63*57 points or 64*64 points. Height of breast is 12cm, radius is 6cm. To add tumors we change object function at that point ( at 3 GHz)(See[4]) For obj. func. of chest we have used [5].

12. Config 1 – Free Space

13. Config 2 – PEC

14. Config 3 – Two Layered Medium

16. CONCLUSION Early detection of breast cancer has a great importance Using qualitative methods is better because: 1) It is faster 2) Its noise immunity is high But they also: 1) Requires large information for solution 2) Has some problems with their assumptions Future work: 1) 3D vectoral configurations 2) New procedures to automaticly decide for tumor…

17. REFERENCES [1] Review of Electromagnetic Techniques for Breast Cancer Detection” whose authors are Hassan AM, El-Shenawee M, from IEEE REVIEWS IN BIOMEDICAL ENGINEERING, VOL. 4, 2011. [2] Y. Grisel, V. Mouysset, P.-A. Mazet, and J.-P. Raymond, “Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements,” Inverse Problems, vol. 28, no. 5, p. 055003, 2012. [3] A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford University Press, Oxford, 2008. [4] Lazebnik, M.; Popovic, D.; McCartney, L.; Watkins, C. B.; Lindstrom, M. J.; Harter, J.; Sewall, S.; Ogilvie, T.; Magliocco, A.; Breslin, T. M. & et al A large-scale study of the ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries Physics in Medicine and Biology, IOP Publishing, 2007, 52, 6093-6115 [5] S. Gabriel, R. Lau, and C. Gabriel, “The dielectric properties of biological tissues: Iii. parametric models for the dielectric spectrum of tissues,” Phys. Med. Biol, vol. 41, p. 22712293, 1996.

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