A wavelet multi-scale method for the inverse problem of diffuse optical tomography

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:289

Article

Dubot, Fabien^1,2  Favennec, Yann²  Rousseau, Benoit²  Rousse, Daniel R.¹ 

[1] Ecole Technol Super, Chaire Rech Ind Technol Energie & Efficacite Ener, Montreal, PQ H3C 1K3, Canada

[2] LTN, UMR CNRS 6607, F-44306 Nantes 3, France

关键词: Optical tomography;    Wavelet multi-scale method;    Inversion;    L-BFGS algorithm;    Optical properties;   

DOI  :  10.1016/j.cam.2015.01.023

来源: Elsevier

【 摘 要 】

This paper deals with the estimation of optical property distributions of participating media from a set of light sources and sensors located on the boundaries of the medium. This is the so-called diffuse optical tomography problem. Such a non-linear ill-posed inverse problem is solved through the minimization of a cost function which depends on the discrepancy, in a least-square sense, between some measurements and associated predictions. In the present case, predictions are based on the diffuse approximation model in the frequency domain while the optimization problem is solved by the L-BFGS algorithm. To cope with the local convergence property of the optimizer and the presence of numerous local minima in the cost function, a wavelet multi-scale method associated with the L-BFGS method is developed, implemented, and validated. This method relies on a reformulation of the original inverse problem into a sequence of sub-inverse problems of different scales using wavelet transform, from the largest scale to the smallest one. Numerical results show that the proposed method brings more stability with respect to the ordinary L-BFGS method and enhances the reconstructed images for most of initial guesses of optical properties. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free