Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method

Abstract

We presents a Born; iterative method, for reconstructing optical properties of turbid media by means of frequency-domain data. The approach is based on iterative solution of a linear perturbation equation, which is derived from the integral from of the Helmholtz wave equation for photon-density waves in each iteration the total field and the associated weight matrix are recalculated based on the previous reconstructed image. We then obtain a new estimate by solving the updated perturbation equation. The forward solution, also based on a Helmholtz equation, is obtained by a multigrid finite difference method. The inversion is carried out through a Tikhonov regularized optimization process by the conjugate gradient descent method. Using this method, we first reconstruct the distribution of the complex wave numbers in a test medium, from which the absorption and the scattering distributions are then derived. Simulation results with two-dimensional test media have shown that this method can yield quantitatively (in terms of coefficient valued) as well as qualitatively (in terms of object location and shape) accurate reconstructions of absorption and scattering distributions in cases in which the first-order Born approximation cannot work well. Both full-angle and limited-angle measurement schemes have been simulated to examine the effect of the location of detectors and sources. The robustness of the algorithm to noise has also been evaluated.

Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy

“…This is the basis of image reconstruction algorithms in which an image of Dl a (i.e., the vector x) can be obtained from a set of measurements (i.e., the vector y) through inversion of the matrix A (i.e., the effective pathlengths L i,j ). While several advanced imaging algorithms have been developed-including analytic diffraction tomography approaches (Cheng and Boas, 1998;Li et al, 1997;Matson and Liu, 1999;Schotland, 1997), perturbation approaches (Arridge and Schweiger, 1995;Barbour et al, 1995;O'Leary et al, 1995;Schotland et al, 1993;Yao et al, 1997), the Taylor series expansion approach (Jiang et al, 1996;Paulsen and Jiang, 1995), gradient-based iterative techniques (Arridge and Schweiger, 1998), elliptic systems method (ESM) (Gryazin et al, 1999;Klibanov et al, 1997), and Bayesian conditioning (Barnett et al, 2003;Eppstein et al, 1999) -the most widely used methods for diffuse optical functional brain imaging incorporate a semiinfinite forward model (Kienle and Patterson, 1997a;Patterson et al, 1989) and either backprojection (Colak et al, 1997;Franceschini et al, 2000;Maki et al, 1995, Walker et al, 1997 or perturbation approaches (Arridge, 1999).…”

Three-dimensional diffuse optical mammography with ultrasound localization in a human subject

“…[40][41][42][43][44][45][46][47][48] We have chosen to follow a Green's function ͑or adjoint͒ method. [15][16][17][18]27,28 The inverse problem, therefore, is formulated in the following way:…”

“…A variety of methods have been developed for DOT. These include fits to analytic solutions, [1][2][3] backprojection methods, [4][5][6][7] diffraction tomography in k-space, [8][9][10][11][12][13][14] perturbation approaches, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] elliptic systems method ͑ESM͒, [31][32][33] and a direct method. 34 All of these approaches have various advantages and disadvantages.…”

An Efficient Numerical Method for General $L_{p}$ Regularization in Fluorescence Molecular Tomography

“…The corresponding forward model is nonlinear and the reconstruction is typically achieved by iterative optimization methods that are based on the first-order approximation of the forward model, that is, the Jacobian. A variety of iterative procedures such as the Born iterative method [10], the coodinate descent algorithm [11], the Gauss-Newton method [12], the truncated-Newton method [13], [14], the Levenberg-Marquardt method [15]- [17], the BFGS method [18], [19], and the nonlinear conjugate gradient method [20] have been studied. When the goal is solely to recover the fluorescent probe concentration, a reasonable approximation is neglect the change in absorption and scattering due to the presence of the fluorophores.…”