Asymptotic Formulas for Thermography Based Recovery of Anomalies
Habib Ammari 1*, Anastasia Kozhemyak 2, Darko Volkov 31 Laboratoire Ondes et Acoustique, CNRS UMR 7587, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France.
2 Centre de Mathematiques Appliquees, CNRS UMR 7641, Ecole Polytechnique, 91128 Palaiseau, France.
3 Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester MA 01609, USA.
Received 29 April 2008; Accepted (in revised version) 27 August 2008
We start from a realistic half space model for thermal imaging, which we then use to develop a mathematical asymptotic analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design noniterative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.AMS subject classifications: 35R20, 35B30
Key words: Thermography, imaging, asymptotic formulas, small anomalies, direct imaging algorithms, half-space problem.
Email: email@example.com (H. Ammari), firstname.lastname@example.org (A. Kozhemyak), email@example.com (D. Volkov)