Frontiers in carbohydrate research-1/ Millane

x, 296 hal.: ill.; 21 cm

Frontiers in carbohydrate research-1/ Millane

x, 296 hal.: ill.; 21 cm

Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography

Optical di#usion tomography is a technique for imaging a highly scattering medium using measurements of the transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a very di#cult nonlinear inverse problem. Bayesian approaches are e#ective, but are computationally expensive, especially for threedimensional imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of non-quadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical di#usion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality. Keywords -- optical di#usion tomography, Bayesian image reconstruction, nonlinear multigrid optimization, multiresolution image reconstruction Corresponde..

Nonlinear Multigrid Algorithms for Bayesian Optical Diffusion Tomography

Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality

Macromolecular phasing using diffraction from multiple crystal forms

A phasing algorithm for macromol­ecular crystallography is proposed that utilizes diffraction data from multiple crystal forms – crystals of the same mol­ecule with different unit-cell packings (different unit-cell parameters or space-group symmetries). The approach is based on the method of iterated projections, starting with no initial phase information. The practicality of the method is demonstrated by simulation using known structures that exist in multiple crystal forms, assuming some information on the mol­ecular envelope and positional relationships between the mol­ecules in the different unit cells. With incorporation of new or existing methods for determination of these parameters, the approach has potential as a method for ab initio phasing

Three-dimensional Bayesian optical diffusion tomography with experimental data

g in the heavily scattering tissue environment is necessary. We previously reported accurate and eff icient inversions for two-dimensional (2-D) test problems, using nonlinear optimization in a Bayesian framework. 3,4 Others have reported iterative approaches based on a 2-D diffusion equation forward model with experimental data. 5,6 Whereas the validity of a 2-D diffusion model for realistic problems has been investigated and corrections proposed, it is clear that, in general, accounting for out-of-plane scattering will require a 3-D solution. 7 Here we extend our previous 2-D Bayesian formulation and iterative coordinate descent optimization method for absorption imaging to three dimensions, and we address the problem of estimating source -- detector coupling, the background diffusion coeff icient, and detector noise variance, thereby circumventing the need for difficult and inconvenient calibration measurements of homogeneous phantoms. The estimation of source -- detector