EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

First order algorithms in variational image processing

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form ${\cal D}(Ku) + \alpha {\cal R} (u) \rightarrow \min_u$ ; where the functional ${\cal D}$ is a data fidelity term also depending on some input data $f$ and measuring the deviation of $Ku$ from such and ${\cal R}$ is a regularization functional. Moreover $K$ is a (often linear) forward operator modeling the dependence of data on an underlying image, and $\alpha$ is a positive regularization parameter. While ${\cal D}$ is often smooth and (strictly) convex, the current practice almost exclusively uses nonsmooth regularization functionals. The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof or $\ell_1$-norms of coefficients arising from scalar products with some frame system. The efficient solution of such variational problems in imaging demands for appropriate algorithms. Taking into account the specific structure as a sum of two very different terms to be minimized, splitting algorithms are a quite canonical choice. Consequently this field has revived the interest in techniques like operator splittings or augmented Lagrangians. Here we shall provide an overview of methods currently developed and recent results as well as some computational studies providing a comparison of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure

Improved Quantification of Small Objects in Near-Infrared Diffuse Optical Tomography

Diffuse optical tomography allows quantification of hemoglobin, oxygen saturation, and water in tissue, and the fidelity in this quantification is dependent on the accuracy of optical properties determined during image reconstruction. In this study, a three-step algorithm is proposed and validated that uses the standard Newton minimization with Levenberg-Marquardt regularization as the first step. The second step is a modification to the existing algorithm using a two-parameter regularization to allow lower damping in a region of interest as compared to background. This second stage allows the recovery of the actual size of an inclusion. A region-based reconstruction is the final third step, which uses the estimated size and position information from step 2 to yield quantitatively accurate average values for the optical parameters. The algorithm is tested on simulated and experimental data and is found to be insensitive to object contrast and position. The percentage error between the true and the average recovered value for the absorption coefficient in test images is reduced from 47 to 27% for a 10-mm inclusion, from 38 to 13% for a 15-mm anomaly, and from 28 to 5.5% for a 20-mm heterogeneity. Simulated data with absorbing and scattering heterogeneities of 15 mm diam located in different positions show recovery with less than 15% error in absorption and 6% error in reduced scattering coefficients. The algorithm is successfully applied to clinical data from a subject with a breast abnormality to yield quantitatively increased absorption coefficients, which enhances the contrast to 3.8 compared to 1.23 previously

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'

Spatially-Dense, Multi-Spectral, Frequency-Domain Diffuse Optical Tomography of Breast Cancer

Diffuse optical tomography (DOT) employs near-infrared light to image the concentration of chromophores and cell organelles in tissue and thereby providing access to functional parameters that can differentiate cancerous from normal tissues. This thesis describes research at the bench and in the clinic that explores and identifies the potential of DOT breast cancer imaging. The bench and clinic instrumentation differ but share important features: they utilize a very large, spatially dense, set of source-detector pairs (10E7) for imaging in the parallel-plate geometry. The bench experiments explored three-dimensional (3D) image resolution and fidelity as a function of numerous parameters and also ascertained the effects of a chest wall phantom. The chest wall is always present but is typically ignored in breast DOT. My experiments clarified chest wall influences and developed schemes to mitigate these effects. Mostly, these schemes involved selective data exclusion, but their efficacy also depended on reconstruction approach. Reconstruction algorithms based on analytic (fast) Fourier inversion and linear algebraic techniques were explored. The clinical experiments centered around a DOT instrument that I designed, constructed, and have begun to test (in-vitro and in-vivo). This instrumentation offers many features new to the field. Specifically, the imager employs spatially-dense, multi-spectral, frequency-domain data; it possesses the world\u27s largest optical source-detector density yet reported, facilitated by highly-parallel CCD-based frequency-domain imaging based on gain-modulation heterodyne detection. The instrument thus measures both phase and amplitude of the diffusive light waves. Other features include both frontal and sagittal breast imaging capabilities, ancillary cameras for measurement of breast boundary profiles, real-time data normalization, and mechanical improvements for patient comfort. The instrument design and construction is my most significant contribution, but first imaging experiments with tissue phantoms and of cancer bearing breasts were also carried out. A parallel effort with simulated data has yielded important information about new reconstruction regularization issues that arise when phase and amplitude are measured. With these gains in device implementation and DOT reconstruction, my research takes valuable steps towards bringing this novel imaging technique closer to clinical utilization

Computational Inverse Problems

Inverse problem typically deal with the identification of unknown quantities from indirect measurements and appear in many areas in technology, medicine, biology, finance, and econometrics. The computational solution of such problems is a very active, interdisciplinary field with close connections to optimization, control theory, differential equations, asymptotic analysis, statistics, and probability. The focus of this workshop was on hybrid methods, model reduction, regularization in Banach spaces, and statistical approaches