Diffuse optical tomography through solving a system of quadratic equations: theory and simulations

This paper discusses the iterative solution of the nonlinear problem of optical tomography. In the established forward model-based iterative image reconstruction (MOBIIR) method a linear perturbation equation containing the first derivative of the forward operator is solved to obtain the update vector for the optical properties. In MOBIIR, the perturbation equation is updated by recomputing the first derivative after each update of the optical properties. In the method presented here a nonlinear perturbation equation, containing terms up to the second derivative, is used to iteratively solve for the optical property updates. Through this modification, reconstructions with reasonable contrast recovery and accuracy are obtained without the need for updating the perturbation equation and therefore eliminating the outer iteration of the usual MOBIIR algorithm. To improve the performance of the algorithm the outer iteration is reintroduced in which the perturbation equation is recomputed without re-estimating the derivatives and with only updated computed data. The system of quadratic equations is solved using either a modified conjugate gradient descent scheme or a two-step linearized predictor-corrector scheme. A quick method employing the adjoint of the forward operator is used to estimate the derivatives. By solving the nonlinear perturbation equation it is shown that the iterative scheme is able to recover large contrast variations in absorption coefficient with improved noise tolerance in data. This ability has not been possible so far with linear algorithms. This is demonstrated by presenting results of numerical simulations from objects with inhomogeneous inclusions in absorption coefficient with different contrasts and shapes.

[1]  S. Arridge.  Photon-measurement density functions. Part I: Analytical forms. , 1995, Applied optics.

[2]  R M Vasu,et al.  Diffuse optical tomography using intensity measurements and the a priori acquired regions of interest: theory and simulations , 2005, Physics in medicine and biology.

[3]  B. Pogue,et al.  Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast. , 2001, Radiology.

[4]  S. Arridge,et al.  Optical imaging in medicine: II. Modelling and reconstruction , 1997, Physics in medicine and biology.

[5]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[6]  M. Schweiger,et al.  Gauss–Newton method for image reconstruction in diffuse optical tomography , 2005, Physics in medicine and biology.

[7]  S. Mohanty,et al.  Measurement of optical transport properties of normal and malignant human breast tissue. , 2001, Applied optics.

[8]  K. Paulsen,et al.  Spatially varying optical property reconstruction using a finite element diffusion equation approximation. , 1995, Medical physics.

[9]  M. Schweiger,et al.  A finite element approach for modeling photon transport in tissue. , 1993, Medical physics.

[10]  A. Klose,et al.  Optical tomography using the time-independent equation of radiative transfer-Part 1: Forward model , 2002 .

[11]  Rob S. MacLeod,et al.  Inverse electrocardiography by simultaneous imposition of multiple constraints , 1999, IEEE Transactions on Biomedical Engineering.

[12]  Oliver Dorn,et al.  A transport-backtransport method for optical tomography , 1998 .

[13]  George H. Weiss,et al.  The continuous-time random walk description of photon motion in an isotropic medium , 1998 .

[14]  S. Nash,et al.  Linear and Nonlinear Programming , 1987 .

[15]  Alexander D. Klose,et al.  Gradient-based iterative image reconstruction scheme for time-resolved optical tomography , 1999, IEEE Transactions on Medical Imaging.

[16]  William Rundell,et al.  A Second Degree Method for Nonlinear Inverse Problems , 1999, SIAM J. Numer. Anal..

[17]  Yukio Yamada,et al.  LIGHT-TISSUE INTERACTION AND OPTICAL IMAGING IN BIOMEDICINE , 1995 .

[18]  E. Sevick-Muraca,et al.  Truncated Newton's optimization scheme for absorption and fluorescence optical tomography: Part I theory and formulation. , 1999, Optics express.

[19]  A. Klose,et al.  Quasi-Newton methods in optical tomographic image reconstruction , 2003 .

[20]  S Arridge,et al.  A gradient-based optimisation scheme foroptical tomography. , 1998, Optics express.

[21]  E. Miller,et al.  Tomographic optical breast imaging guided by three-dimensional mammography. , 2003, Applied optics.

[22]  M. Schweiger,et al.  The finite element method for the propagation of light in scattering media: boundary and source conditions. , 1995, Medical physics.

[23]  D. Boas,et al.  Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography. , 1995, Optics letters.

[24]  D. Boas,et al.  Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head. , 2002, Optics express.

[25]  J. Kottmann,et al.  Spectral response of plasmon resonant nanoparticles with a non-regular shape. , 2000, Optics express.

[26]  M. Schweiger,et al.  Photon-measurement density functions. Part 2: Finite-element-method calculations. , 1995, Applied optics.

[27]  S R Arridge,et al.  Recent advances in diffuse optical imaging , 2005, Physics in medicine and biology.