Seungseok Oh

Fluorescence optical diffusion tomography

A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing the fluorescent agent Indocyanine Green.

A general framework for nonlinear multigrid inversion

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional (3D) partial differential equation. For these applications, image reconstruction is particularly difficult because the forward problem is both nonlinear and computationally expensive to evaluate. We propose a general framework for nonlinear multigrid inversion that is applicable to a wide variety of inverse problems. The multigrid inversion algorithm results from the application of recursive multigrid techniques to the solution of optimization problems arising from inverse problems. The method works by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid inversion algorithm efficiently computes the solution to the desired fine-scale inversion problem. Importantly, the new algorithm can greatly reduce computation because both the forward and inverse problems are more coarsely discretized at lower resolutions. An application of our method to Bayesian optical diffusion tomography with a generalized Gaussian Markov random-field image prior model shows the potential for very large computational savings. Numerical data also indicates robust convergence with a range of initialization conditions for this nonconvex optimization problem.

Three-dimensional Bayesian optical diffusion tomography with experimental data

Reconstructions of a three-dimensional absorber embedded in a scattering medium by use of frequency domain measurements of the transmitted light in a single source-detector plane are presented. The reconstruction algorithm uses Bayesian regularization and iterative coordinate descent optimization, and it incorporates estimation of the detector noise level, the source-detector coupling coefficient, and the background diffusion coefficient in addition to the absorption image. The use of multiple modulation frequencies is also investigated. The results demonstrate the utility of this algorithm, the importance of a three-dimensional model, and that out-of-plane scattering permits recovery of three-dimensional features from measurements in a single plane.

Source–detector calibration in three-dimensional Bayesian optical diffusion tomography

Optical diffusion tomography is a method for reconstructing three-dimensional optical properties from light that passes through a highly scattering medium. Computing reconstructions from such data requires the solution of a nonlinear inverse problem. The situation is further complicated by the fact that while reconstruction algorithms typically assume exact knowledge of the optical source and detector coupling coefficients, these coupling coefficients are generally not available in practical measurement systems. A new method for estimating these unknown coupling coefficients in the three-dimensional reconstruction process is described. The joint problem of coefficient estimation and three-dimensional reconstruction is formulated in a Bayesian framework, and the resulting estimates are computed by using a variation of iterative coordinate descent optimization that is adapted for this problem. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients as well as the coupling coefficients. A simple experimental result validates the approach.

Multigrid tomographic inversion with variable resolution data and image spaces

A multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed. Since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements, the proposed algorithm further reduces the computation relative to conventional multigrid approaches, which change only the image space resolution at coarse scales. The advantage is particularly important for data-rich applications, where data resolutions may differ for different scales. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography with a generalized Gaussian Markov random field image prior are presented, both with a Poisson noise model and with a quadratic data term. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent method and a multigrid method with fixed-data resolution

Multigrid algorithms for optimization and inverse problems

A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction can be formulated as the solution to a non-quadratic optimization problem. In this paper, we discuss the use of nonlinear multigrid methods as both tools for optimization and algorithms for the solution of difficult inverse problems. In particular, we review some existing methods for directly formulating optimization algorithm in a multigrid framework, and we introduce a new method for the solution of general inverse problems which we call multigrid inversion. These methods work by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid optimization methods can efficiently compute the solution to a desired fine scale optimization problem. Importantly, the multigrid inversion algorithm can greatly reduce computation because both the forward and the inverse problems are more coarsely discretized at lower resolutions. An application of our method to optical diffusion tomography shows the potential for very large computational savings.

Multigrid inversion algorithms with applications to optical diffusion tomography

In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. In multigrid inversion, the problem is adjusted at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of cost functional across resolutions. At each resolution, both the forward and inverse problems are discretized at the lower resolution; thus reducing computation. Simulation results for the problem of optical diffusion tomography indicate that multigrid inversion can dramatically reduce computation in this application.

Adaptive nonlinear multigrid inversion with applications to Bayesian optical diffusion tomography

We previously proposed a general framework for nonlinear multi-grid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. The method has the potential for very large computational savings and robust convergence. In this paper, multigrid inversion is further extended to adaptively allocate computation to the scale at which the algorithm can best reduce the cost. We applied the proposed method to solve the problem of optical diffusion tomography in a Bayesian framework, and our simulation results indicate that the adaptive scheme can improve computational efficiency in this application.

Nonlinear multigrid inversion

In this paper, we propose a general framework for nonlinear multigrid inversion applicable to any inverse problem in which the forward model can be naturally represented at differing resolutions. In multigrid inversion, the problem is adjusted to be solved at each resolution by using the solutions at both finer and coarser resolutions. To do this, we formulate a consistent set of coarse scale cost functionals to ultimately reduce the finest scale one. At each resolution, both the forward model and inverse problems are discretized at the lower resolution; thus reducing computation. Our simulation results for the application of optical diffusion tomography indicate the potential for fast and robust convergence.

Multigrid inversion algorithms for Poisson noise model-based tomographic reconstruction

A multigrid inversion approach is proposed to solve Poisson noise model-based inverse problems. The algorithm works by moving up and down in resolution with a set of coarse scale cost functions, which incorporates a coarse scale Poisson mean defined in low resolution data and image spaces. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography are presented. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent (ICD) method.