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Asymptotic Formulas for Thermography Based Recovery of Anomalies

Summary: Asymptotic Formulas for Thermography Based Recovery
of Anomalies
Habib Ammari
Anastasia Kozhemyak
Darko Volkov §
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 reconstruc-
tion algorithms. We seek to reconstruct thermal anomalies only through their rough
features. 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 de-
tection algorithms. We show on numerical simulations evidence that they are accurate
and robust . Additionally, we provide a mathematical model for ultrasonic temperature
imaging, an important technique in cancerous tissue ablation therapy.
1 Introduction
Medical thermal imaging has become a procedure of choice in the screening for breast, skin,
or liver cancer [10]. It has the ability to identify various stages of disease development, and
can pick up early stages which usually elude traditional anatomical examinations. Thermal
imaging relies on the fact that chemical and blood vessel activity in pre-cancerous tissue


Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique


Collections: Mathematics