Hstau Y. Liao

Sparse representations for limited data tomography

In limited data tomography, with applications such as electron microscopy and medical imaging, the scanning views are within an angular range that is often both limited and sparsely sampled. In these situations, standard algorithms produce reconstructions with notorious artifacts. We show in this paper that a sparsity image representation principle, based on learning dictionaries for sparse representations of image patches, leads to significantly improved reconstructions of the unknown density from its limited angle projections. The presentation of the underlying framework is complemented with illustrative results on artificial and real data.

Automated estimation of the parameters of Gibbs priors to be used in binary tomography

Image modeling using Gibbs priors was previously shown, based on experiments, to be effective in image reconstruction problems. This motivated us to evaluate three methods for estimating the priors. Two of them accurately recover the parameters of the priors; however, all of them are useful for binary tomography. This is demonstrated by two sets of experiments: in one the images are from a Gibbs distribution and in the other they are typical cardiac phantom images.

A coordinate ascent approach to tomographic reconstruction of label images from a few projections

Our aim is to produce a tessellation of space into small voxels and, based on only a few tomographic projections of an object, assign to each voxel a label from a small predetermined set that indicates one of the components of interest constituting the object. Traditional methods are not reliable due to, among other reasons, the low number of projections. We postulate a low level prior knowledge regarding the underlying distribution of label images, and then directly estimate a label image based on the prior and the projections. We use a coordinate ascent approach for the estimation.

A method for reconstructing label images from a few projections, as motivated by electron microscopy

Our aim is to produce a tessellation of space into small voxels and, based on only a few tomographic projections of an object, assign to each voxel a label that indicates one of the components of interest constituting the object. Traditional methods are not reliable in applications, such as electron microscopy in which (due to the damage by radiation) only a few projections are available. We postulate a low level prior knowledge regarding the underlying distribution of label images, and then directly estimate the label image based on the prior and the projections. We use a relatively efficient approximation to a global search for the optimal estimate.

Reconstruction of label images from a few projections as motivated by electron microscopy

Our aim is to utilize electron micrographs of biological macromolecules to produce a tessellation of space into small voxels, each labeled as containing ice, protein, or RNA. Traditional approaches first assign to each voxel a gray value (associated with the density of atoms in the voxel) based on the micrographs and then threshold this gray value image to obtain the label image. A problem with this approach is that at higher resolutions (smaller voxels) the ranges of atom densities corresponding to different labels greatly overlap, and so the label image will need to be of low resolution in order to be reliable. Another difficulty is that, due to the destructive nature of the electron microscope, only a few projections can be taken. We propose to overcome these difficulties by first postulating some low level prior knowledge (based on the general nature of macromolecules) regarding the underlying distribution of label images, and then estimating directly a particular label image based on this prior distribution together with the micrographs. Here we report on our first experiments aimed at evaluating this approach.

Optimized algebraic reconstruction technique for generation of grain maps based on three-dimensional x-ray diffraction (3DXRD)

Recently, an algebraic reconstruction method has been presented for generation of three-dimensional (3D) maps of the grain boundaries within polycrystals. The grains are mapped layer by layer in a nondestructive way by diffraction with hard x rays. We optimize the algorithm by means of simulations and discuss ways to automate the analysis. The use of generalized Kaiser-Bessel functions as basis functions is shown to be superior to a conventional discretization in terms of square pixels. The algorithm is reformulated as a block-iterative method in order to incorporate the instrumental point-spread function and, at the same time, to avoid the need to store the set of equations. The first reconstruction of a full layer and two neighboring 3D grains from experimental data are demonstrated.

Discrete tomography with a very few views, using Gibbs priors and a Marginal Posterior Mode approach

Abstract We propose a marginal posterior mode (MPM) approach to the reconstruction of 3D label images from only a few projections, using Gibbs priors. This work is motivated by electron tomography of biological macromolecules. The strategy is to produce a tessellation of space into small voxels and label each voxel as containing ice, protein, or ribosomal nucleic acid (RNA), based on (because of the radiation damage) only a few electron micrographs.

Tomographic Reconstruction of Label Images from a Few Projections

Abstract Our aim is to produce a tessellation of space into small voxels and, based on tomo-graphic projections, assign to each one of them a label from a small predetermined set. The traditional approach first assigns to each voxel a gray value based on the projections and then thresholds this gray value image to obtain the label image. There are problems with this approach. For example, in electron microscopy of macromolecules at high resolution (small voxels) the ranges of atom densities corresponding to different labels greatly overlap, and so the label image has to be of low resolution in order to be reliable. Another difficulty is that, due to the destructive nature of the electron microscope, only a few projections can be taken. We propose to overcome such difficulties by first postulating some low level prior knowledge (in electron microscopy this would be based on the general nature of macromolecules) regarding the underlying distribution of label images, and then estimating directly a particular label image based on this prior distribution together with the projections. Here we report on our early experiments aimed at evaluating this approach.

Optimization of an algebraic reconstruction technique for generation of grain maps based on diffraction data

Recently an algebraic reconstruction method, 2D-ART, has been presented for generation of three-dimensional maps of the grain boundaries within polycrystals. The grains are mapped layer-by-layer in a non-destructive way by diffraction with hard x-rays. Here we optimize the algorithm by means of simulations and discuss ways to automate the analysis. The use of generalized Kaiser-Bessel functions as basis functions is shown to be superior to a conventional discretization in terms of square pixels. The algorithm is reformulated as a block-iterative method in order to incorporate the instrumental point-spread-function and, at the same time, to avoid the need to store the set of equations. The first reconstruction of a full layer from experimental data is demonstrated.

Reconstruction by direct labeling in electron tomography, using Gibbs priors and a marginal posterior mode approach

We propose a new direct labeling approach to electron tomography of biological macromolecules, using Gibbs priors and the marginal posterior mode (MPM) estimator. The aim is to produce a tessellation of space into small voxels and label each voxel as containing ice, protein, or ribosomal nucleic acid (RNA), based on only a few electron micrographs. We show that the MPM estimator outperforms the maximum a posteriori probability (MAP) estimator, which has been the standard not only for this type of application but also for most computer vision problems.