TY - JOUR T1 - Asymptotic Formulas for Thermography Based Recovery of Anomalies JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 18 EP - 42 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6014.html KW - Thermography, imaging, asymptotic formulas, small anomalies, direct imaging algorithms, half-space problem. AB -

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.