Reconstruction of the perfusion coefficient from temperature measurements using the conjugate gradient method

ABSTRACT

We consider the inverse bio-heat transfer problem to determine the space- and time-dependent perfusion coefficient from temperature measurements. In this formulation, the problem is fully determined and the coefficient is identifiable if and only if the temperature has dense support. However, the problem is still ill-posed since small errors in the measured temperature cause large errors in the output perfusion coefficient due to the numerical differentiation of noisy data involved which represents an unstable procedure. In order to overcome this difficulty and restore stability, we employ for the first time the conjugate gradient method (CGM) for solving the inverse problem under investigation. Regularization is achieved by stopping the iteration process at an appropriate threshold dictated by the discrepancy principle. Numerical results show that the CGM is accurate and reasonably stable in retrieving the perfusion coefficient. Moreover, comparison with other methods shows improved efficiency and stability in inverting noisy data.

KEYWORDS:

• Inverse problem
• bio-heat equation
• ill-posed problem
• conjugate gradient method
• perfusion coefficient

2010 AMS Subject Classifications:

• 65M32
• 35K05

Acknowledgments

K. Cao would like to thank the University of Leeds and the China Scholarship Council for supporting his Ph.D. studies at the University of Leeds.

Disclosure statement

No potential conflict of interest was reported by the authors.