Yuqi Yao

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

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.

A wavelet-based multiresolution regularized least squares reconstruction approach for optical tomography

The authors present a wavelet-based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using a multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest (ROIs) from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level a regularized least squares solution is obtained using the conjugate gradient descent method. This approach has been applied to continuous wave data calculated based on the diffusion approximation of several two-dimensional (2-D) test media. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method

We present an iterative total least-squares algorithm for computing images of the interior structure of highly scattering media by using the conjugate gradient method. For imaging the dense scattering media in optical tomography, a perturbation approach has been described previously [Y. Wang et al., Proc. SPIE 1641, 58 (1992); R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87-120], which solves a perturbation equation of the form W delta x = delta I. In order to solve this equation, least-squares or regularized least-squares solvers have been used in the past to determine best fits to the measurement data delta I while assuming that the operator matrix W is accurate. In practice, errors also occur in the operator matrix. Here we propose an iterative total least-squares (ITLS) method that minimizes the errors in both weights and detector readings. Theoretically, the total least-squares (TLS) solution is given by the singular vector of the matrix [W/ delta I] associated with the smallest singular value. The proposed ITLS method obtains this solution by using a conjugate gradient method that is particularly suitable for very large matrices. Simulation results have shown that the TLS method can yield a significantly more accurate result than the least-squares method.

SIMULTANEOUS RECONSTRUCTION OF ABSORPTION AND SCATTERING DISTRIBUTIONS IN TURBID MEDIA USING A BORN ITERATIVE METHOD

In this paper, we present a Born Iterative Method for imaging optical properties of turbid media using frequency-domain data. In each iteration, the incident field and the associated weight matrix are first recalculated based on the previous reconstructed image. A new estimate is then obtained by a multigrid finite difference method. The inversion is carried out through a Tikhonov regularized optimization process using the conjugate gradient descent. Using this method, the distribution of the complex wavenumbers in a test medium is first reconstructed, from which the absorption and scattering distributions are then derived. Simulation results have shown that this method can yield quantitatively quite accurate reconstruction even when a strong perturbation exists between the actual medium and an assumed homogeneous background medium, in which case the Born approximation cannot work well. Both full-angle and limited angle measurement schemes have been simulated to understand the effect of the location of detectors and sources.

Sensitivity studies for imaging a spherical object embedded in a spherically symmetric, two-layer turbid medium with photon-density waves

We present analytic expressions for the amplitude and phase of photon-density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. This layered structure is a crude model of multilayered tissues whose absorption and scattering coefficients lie within a range reported in the literature for most tissue types. The embedded object simulates a pathology, such as a tumor. The normal-mode-series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field at points in the outer layer at a fixed distance from the origin when the object is present and when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media with different absorption and scattering properties, we determine the modulation frequency that achieves an optimal compromise between signal-detection reliability and sensitivity to the presence of an object, the minimum detectable object radius, and the smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our results indicate that (l) enhanced sensitivity to the object is achieved when the outer layer is more absorbing or scattering than the inner layer; (2) sensitivity to the object increases with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude measurements are proportionally more sensitive to a change in absorption, phase measurements are proportionally more sensitive to a change in scattering, and phase measurements exhibit a much greater capacity for distinguishing an absorption perturbation from a scattering perturbation.

Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium

We present an analytic solution to the amplitude and phase distributions of photon density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. The normal mode series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field on the surface of the outer layer when the object is present to when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media which are different in their absorption and scattering properties, we determine: i) the modulation frequency that achieves an optimal compromise between signal detection reliability and sensitivity to the presence of object; ii) the minimum detectable object radius, iii) the smallest detectable change in its absorption coefficient and iv) scattering coefficient for a fixed object size. A discussion of the qualitative and quantitative findings is given.

Multiresolution regularized least squares image reconstruction based on wavelet in optical tomography

In this paper, we present a wavelet based multigrid approach to solve the perturbation equation encountered in optical tomogrpahy. With this scheme, the unkown image, the data, as well as weight matrix are all represented by wavelet expansions, and thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level, a regularized least squares solution is obtained using a conjugate gradient descent method. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

Frequency domain fluorescence optical imaging using a finite element method

In this paper, a reconstruction algorithm for fluorescence yield and lifetime imaging in dense scattering media is formulated and implemented. Two frequency domain radiation transport equations based on the diffusion approximation are used to model the migration of excitation and emitted photons. In the forward formulation, a finite element approach, which is specially effective for complex geometries and inhomogeneous distribution of medium properties, is adopted to obtain the required imaging operator and the simulated detector responses related to the photon fluxes on the boundary. Inverse formulation is derived based on the integral form of two diffusion equations. The technique is demonstrated by reconstructing spatial images of heterogenous fluorophore distribution and life time using simulated data obtained from homogeneous and complex (i.e., MRI breast map) media containing objects with fluorophore and with and without added noise.