Nonlinear approach to difference imaging in diffuse optical tomography

Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change. Conventionally, the image reconstruction is based on using difference of the measurements and a linear approximation of the observation model. One of the main benefits of the linearized difference reconstruction is that the approach has a good tolerance to modeling errors, which cancel out partially in the subtraction of the measurements. However, a drawback of the approach is that the difference images are usually only qualitative in nature and their spatial resolution can be weak because they rely on the global linearization of the nonlinear observation model. To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously based on the two datasets. We tested the feasibility of the method with simulations and experimental data from a phantom and studied how the approach tolerates modeling errors like domain truncation, optode coupling errors, and domain shape errors.

Singular value decomposition based computationally efficient algorithm for rapid dynamic near-infrared diffuse optical tomography

PURPOSE

A computationally efficient algorithm (linear iterative type) based on singular value decomposition (SVD) of the Jacobian has been developed that can be used in rapid dynamic near-infrared (NIR) diffuse optical tomography.

METHODS

Numerical and experimental studies have been conducted to prove the computational efficacy of this SVD-based algorithm over conventional optical image reconstruction algorithms.

RESULTS

These studies indicate that the performance of linear iterative algorithms in terms of contrast recovery (quantitation of optical images) is better compared to nonlinear iterative (conventional) algorithms, provided the initial guess is close to the actual solution. The nonlinear algorithms can provide better quality images compared to the linear iterative type algorithms. Moreover, the analytical and numerical equivalence of the SVD-based algorithm to linear iterative algorithms was also established as a part of this work. It is also demonstrated that the SVD-based image reconstruction typically requires O(NN2) operations per iteration, as contrasted with linear and nonlinear iterative methods that, respectively, require O(NN3) and O(NN6) operations, with "NN" being the number of unknown parameters in the optical image reconstruction procedure.

CONCLUSIONS

This SVD-based computationally efficient algorithm can make the integration of image reconstruction procedure with the data acquisition feasible, in turn making the rapid dynamic NIR tomography viable in the clinic to continuously monitor hemodynamic changes in the tissue pathophysiology.

Image correction scheme applied to functional diffuse optical tomography scattering images

We have extended our investigation on the use of a linear algorithm for enhancing the accuracy of diffuse optical tomography (DOT) images, to include spatial maps of the diffusion coefficient. The results show that the corrected images are markedly improved in terms of estimated size, spatial resolution, two-object resolving power, and quantitative accuracy. These image-enhancing effects are significant at expected levels of diffusion-coefficient contrast in tissue and noise levels typical of experimental DOT data. Overall, the types and magnitudes of image-enhancing effects obtained here are qualitatively similar to those seen in previous studies on mu(a) perturbations. The implications for practical implementations of DOT time-series imaging are discussed.

Image correction algorithm for functional three-dimensional diffuse optical tomography brain imaging

We outline a computationally efficient image correction algorithm, which we have applied to diffuse optical tomography (DOT) image time series derived from a magnetic resonance imaging (MRI)-based brain model. Results show that the algorithm increases spatial resolution, decreases spatial bias, and only modestly reduces temporal accuracy for noise levels typically seen in experiment, and produces results comparable to image reconstructions that incorporate information from MRI priors. We demonstrate that this algorithm has robust performance in the presence of noise, background heterogeneity, irregular external and internal boundaries, and error in the initial guess. However, the algorithm introduces artifacts when the absorption and scattering coefficients of the reference medium are overestimated--a situation that is easily avoided in practice. The considered algorithm offers a practical approach to improving the quality of images from time-series DOT, even without the use of MRI priors.

Image quality improvement via spatial deconvolution in optical tomography: time-series imaging

We present the fourth in a series of studies devoted to the issue of improving image quality in diffuse optical tomography (DOT) by using a spatial deconvolution operation that seeks to compensate for the information-blurring property of first-order perturbation algorithms. Our earlier reports consider only static target media. Here we report spatial deconvolution applied to media with time-varying optical properties, as a model of tissue dynamics resulting from varying metabolic demand and modulation of the vascular bed. Issues under study include the influence of deconvolution on the accuracy of the recovered temporal and spatial information. The impact of noise is also explored, and techniques for ameliorating its information-degrading effects are examined. At low noise levels (i.e, < or = 5% of the time-varying signal amplitude), spatial deconvolution markedly improves the accuracy of recovered information. Temporal information is more seriously degraded by noise than is spatial information, and the impact of noise increases with the complexity of the time-varying signal. These effects, however, can be significantly reduced using simple noise suppression techniques (e.g., low-pass filtering). Results suggest that the deconvolution scheme should provide considerable enhancement of the quality of spatiotemporal information recovered from dynamic DOT techniques applied to tissue studies.

Improved accuracy of reconstructed diffuse optical tomographic images by means of spatial deconvolution: two-dimensional quantitative characterization

Systematic characterization studies are presented, relating to a previously reported spatial deconvolution operation that seeks to compensate for the information-blurring property of first-order perturbation algorithms for diffuse optical tomography (DOT) image reconstruction. In simulation results that are presented, this deconvolution operation has been applied to two-dimensional DOT images reconstructed by solving a first-order perturbation equation. Under study was the effect on algorithm performance of control parameters in the measurement (number and spatial distribution of sources and detectors, presence of noise, and presence of systematic error), target (medium shape; and number, location, size, and contrast of inclusions), and computational (number of finite-element-method mesh nodes, length of filter-generating linear system, among others) parameter spaces associated with computation and the use of the deconvolution operators. Substantial improvements in reconstructed image quality, in terms of recovered inclusion location, size, and contrast, are found in all cases. A finding of practical importance is that the method is robust to appreciable differences between the optical coefficients of the media used for filter generation and those of the target media to which the filters are subsequently applied.

Spatial deconvolution technique to improve the accuracy of reconstructed three-dimensional diffuse optical tomographic images

A straightforward spatial deconvolution operation is presented that seeks to invert the information-blurring property of first-order perturbation algorithms for diffuse optical tomography (DOT) image reconstruction. The method that was developed to generate these deconvolving operators, or filters, was conceptually based on the frequency-encoding process used in magnetic resonance imaging. The computation of an image-correcting filter involves the solution of a large system of linear equations, in which known true distributions and the corresponding recovered distributions are compared. Conversely, application of a filter involves only a simple matrix multiplication. Simulation results show that application of this deconvolution operation to three-dimensional DOT images reconstructed by the solution of a first-order perturbation equation (Born approximation) can yield marked enhancement of image quality. In the examples considered, use of image-correcting filters produces obvious improvements in image quality, in terms of both location and mirco(a) of the inclusions. The displacements between the true and recovered locations of an inclusion's centroid location are as small as 1 mm, in an 8-cm-diameter medium with 1.5-cm-diameter inclusions, and the peak value of the recovered micro(a) for the inclusions deviates from the true value by as little as 5%.