Misha E. Kilmer

Tomographic optical breast imaging guided by three-dimensional mammography

We introduce a modified Tikhonov regularization method to include three-dimensional x-ray mammography as a prior in the diffuse optical tomography reconstruction. With simulations we show that the optical image reconstruction resolution and contrast are improved by implementing this x-ray-guided spatial constraint. We suggest an approach to find the optimal regularization parameters. The presented preliminary clinical result indicates the utility of the method.

Wavelet domain image restoration with adaptive edge-preserving regularization

In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.

A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient

We compare, through simulations, the performance of four linear algorithms for diffuse optical tomographic reconstruction of the three-dimensional distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave approximation. The simulation geometry consisted of a coplanar array of sources and detectors at the boundary of a half-space medium. The forward solution matrix is both underdetermined, because we estimate many more absorption coefficient voxels than we have measurements, and ill-conditioned, due to the ill-posedness of the inverse problem. We compare two algebraic techniques, ART and SIRT, and two subspace techniques, the truncated SVD and CG algorithms. We compare three-dimensional reconstructions with two-dimensional reconstructions which assume all inhomogeneities are confined to a known horizontal slab, and we consider two object-based error metrics in addition to mean square reconstruction error. We include a comparison using simulated data generated using a different FDFD method with the same inversion algorithms to indicate how our conclusions are affected in a somewhat more realistic scenario. Our results show that the subspace techniques are superior to the algebraic techniques in localization of inhomogeneities and estimation of their amplitude, that two-dimensional reconstructions are sensitive to underestimation of the object depth, and that an error measure based on a location parameter can be a useful complement to mean squared error.

Optimal linear inverse solution with multiple priors in diffuse optical tomography

A general framework for incorporating single and multiple priors in diffuse optical tomography is described. We explore the use of this framework for simultaneously utilizing spatial and spectral priors in the context of imaging breast cancer. The utilization of magnetic resonance images of water and lipid content as a statistical spatial prior for the diffuse optical image reconstructions is also discussed. Simulations are performed to demonstrate the significant improvement in image quality afforded by combining spatial and spectral priors.

Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography

The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a tensor-based iterative algorithm that simultaneously reconstructs the X-ray attenuation distribution for each energy. We use a multilinear image model rather than a more standard stacked vector representation in order to develop novel tensor-based regularizers. In particular, we model the multispectral unknown as a three-way tensor where the first two dimensions are space and the third dimension is energy. This approach allows for the design of tensor nuclear norm regularizers, which like its 2D counterpart, is a convex function of the multispectral unknown. The solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers approach. Simulation results show that the generalized tensor nuclear norm can be used as a standalone regularization technique for the energy selective (spectral) computed tomography problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent.

Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography

We present a shape-based approach to three-dimensional image reconstruction from diffuse optical data. Our approach differs from others in the literature in that we jointly reconstruct object and background characterization and localization simultaneously, rather than sequentially process for optical properties and postprocess for edges. The key to the efficiency and robustness of our algorithm is in the model we propose for the optical properties of the background and anomaly: We use a low-order parameterization of the background and another for the interior of the anomaly, and we use an ellipsoid to describe the boundary of the anomaly. This model has the effect of regularizing the inversion problem and provides a natural means of including additional physical properties if they are known a priori. A Gauss-Newton-type algorithm with line search is implemented to solve the underlying nonlinear least-squares problem and thereby determine the coefficients of the parameterizations and the descriptors of the ellipsoid. Numerical results show the effectiveness of this method.

A shape-based reconstruction technique for DPDW data

We give an approach for directly localizing and characterizing the properties of a compactly supported absorption coefficient perturbation as well as coarse scale structure of the background medium from a sparsely sampled, diffuse photon density wavefield. Our technique handles the problems of localization and characterization simultaneously by working directly with the data, unlike traditional techniques that require two stages. We model the unknowns as a superposition of a slowly varying perturbation on a background of unknown structure. Our model assumes that the anomaly is delineated from the background by a smooth perimeter which is modeled as a spline curve comprised of unknown control points. The algorithm proceeds by making small perturbations to the curve which are locally optimal. The result is a global, greedy-type optimization approach designed to enforce consistency with the data while requiring the solution to adhere to prior information we have concerning the likely structure of the anomaly. At each step, the algorithm adaptively determines the optimal weighting coefficients describing the characteristics of both the anomaly and the background. The success of our approach is illustrated in two simulation examples provided for a diffuse photon density wave problem arising in a bio-imaging application.

Fast regularized reconstruction of non-uniformly subsampled parallel MRI data

Parallel MR imaging is an effective approach to reduce MR image acquisition time. Non-uniform subsampling allows one to tailor the subsampling scheme for improved image quality at high acceleration factors. However, non-uniform subsampling precludes fast reconstruction schemes such as SENSE, and is more likely to require a regularized solution than reconstruction of uniformly subsampled data demands. This means that one needs to choose a good regularization parameter, typically requiring multiple expensive system solves. Here, we present an efficient LSQR-Hybrid algorithm which simultaneously addresses the need for rapid regularization parameter selection and fast reconstruction. This algorithm can reconstruct non-uniformly subsampled parallel MRI data, with automatic regularization and good image quality, in a time competitive with Cartesian SENSE

Parametric estimation of 3D tubular structures for diffuse optical tomography

We explore the use of diffuse optical tomography (DOT) for the recovery of 3D tubular shapes representing vascular structures in breast tissue. Using a parametric level set method (PaLS) our method incorporates the connectedness of vascular structures in breast tissue to reconstruct shape and absorption values from severely limited data sets. The approach is based on a decomposition of the unknown structure into a series of two dimensional slices. Using a simplified physical model that ignores 3D effects of the complete structure, we develop a novel inter-slice regularization strategy to obtain global regularity. We report on simulated and experimental reconstructions using realistic optical contrasts where our method provides a more accurate estimate compared to an unregularized approach and a pixel based reconstruction.

Quantifying cellular alignment on anisotropic biomaterial platforms.

How do we quantify cellular alignment? Cellular alignment is an important technique used to study and promote tissue regeneration in vitro and in vivo. Indeed, regenerative outcomes are often strongly correlated with the efficacy of alignment, making quantitative, automated assessment an important goal for the field of tissue engineering. There currently exist various classes of algorithms, which effectively address the problem of quantifying individual cellular alignments using Fourier methods, kernel methods, and elliptical approximation; however, these algorithms often yield population distributions and are limited by their inability to yield a scalar metric quantifying the efficacy of alignment. The current work builds on these classes of algorithms by adapting the signal processing methods previously used by our group to study the alignment of cellular processes. We use an automated, ellipse-fitting algorithm to approximate cell body alignment with respect to a silk biomaterial scaffold, followed by the application of the normalized cumulative periodogram criterion to produce a scalar value quantifying alignment. The proposed work offers a generalized method for assessing cellular alignment in complex, two-dimensional environments. This method may also offer a novel alternative for assessing the alignment of cell types with polarity, such as fibroblasts, endothelial cells, and mesenchymal stem cells, as well as nuclei.