Teresa Correia

Selection of regularization parameter for optical topography

The choice of the regularization parameter has a profound effect on the solution of ill-posed inverse problems such as optical topography. We review 11 different methods for selecting the Tikhonov regularization parameter that have been described previously in the literature. We test them on two trial problems, deblurring and optical topography, and conclude that the L-curve method is the method of choice, though in particularly ill-posed problems, generalized cross-validation may provide an alternative.

Fluorescence diffuse optical tomography using the split Bregman method

PURPOSEnStandard image reconstruction methods for fluorescence Diffuse Optical Tomography (fDOT) generally make use of L2-regularization. A better choice is to replace the L2 by a total variation functional that effectively removes noise while preserving edges. Among the wide range of approaches available, the recently appeared Split Bregman method has been shown to be optimal and efficient. Furthermore, additional constraints can be easily included. We propose the use of the Split Bregman method to solve the image reconstruction problem for fDOT with a nonnegativity constraint that imposes the reconstructed concentration of fluorophore to be positive.nnnMETHODSnThe proposed method is tested with simulated and experimental data, and results are compared with those yielded by an equivalent unconstrained optimization approach based on Gauss-Newton (GN) method, in which the negative part of the solution is projected to zero after each iteration. In addition, the method dependence on the parameters that weigh data fidelity and nonnegativity constraints is analyzed.nnnRESULTSnSplit Bregman yielded a reduction of the solution error norm and a better full width at tenth maximum for simulated data, and higher signal-to-noise ratio for experimental data. It is also shown that it led to an optimum solution independently of the data fidelity parameter, as long as the number of iterations is properly selected, and that there is a linear relation between the number of iterations and the inverse of the data fidelity parameter.nnnCONCLUSIONSnSplit Bregman allows the addition of a nonnegativity constraint leading to improve image quality.

Split operator method for fluorescence diffuse optical tomography using anisotropic diffusion regularisation with prior anatomical information

Fluorescence diffuse optical tomography (fDOT) is an imaging modality that provides images of the fluorochrome distribution within the object of study. The image reconstruction problem is ill-posed and highly underdetermined and, therefore, regularisation techniques need to be used. In this paper we use a nonlinear anisotropic diffusion regularisation term that incorporates anatomical prior information. We introduce a split operator method that reduces the nonlinear inverse problem to two simpler problems, allowing fast and efficient solution of the fDOT problem. We tested our method using simulated, phantom and ex-vivo mouse data, and found that it provides reconstructions with better spatial localisation and size of fluorochrome inclusions than using the standard Tikhonov penalty term.

Identification of the optimal wavelengths for optical topography: a photon measurement density function analysis

A method is presented to select the optimal wavelengths for multispectral optical topography, which not only gives good separation between chromophores, absorption, and scattering, but also minimizes the differences between interrogated volumes. This method uses the sum of squared differences to compare photon measurement density functions, which were generated for wavelengths in the near-infrared (NIR) range for a suitable model of tissue optical properties. It is found that including this condition significantly influences the range of optimal wavelengths. However, for the adult human head, the differences between interrogated volumes at NIR wavelengths are very small and image reconstruction is only slightly improved when measurements with overlapping sensitivities are used.

Wavelet-based data and solution compression for efficient image reconstruction in fluorescence diffuse optical tomography

Current fluorescence diffuse optical tomography (fDOT) systems can provide large data sets and, in addition, the unknown parameters to be estimated are so numerous that the sensitivity matrix is too large to store. Alternatively, iterative methods can be used, but they can be extremely slow at converging when dealing with large matrices. A few approaches suitable for the reconstruction of images from very large data sets have been developed. However, they either require explicit construction of the sensitivity matrix, suffer from slow computation times, or can only be applied to restricted geometries. We introduce a method for fast reconstruction in fDOT with large data and solution spaces, which preserves the resolution of the forward operator whilst compressing its representation. The method does not require construction of the full matrix, and thus allows storage and direct inversion of the explicitly constructed compressed system matrix. The method is tested using simulated and experimental data. Results show that the fDOT image reconstruction problem can be effectively compressed without significant loss of information and with the added advantage of reducing image noise.

Quantitative fluorescence diffuse optical tomography in the presence of heterogeneities

In fluorescence diffuse optical tomography (fDOT), the accuracy of reconstructed fluorescence distributions highly depends on the knowledge of the tissue optical heterogeneities for correct modeling of light propagation. Common approaches are to assume homogeneous optical properties or, when structural information is available, assign optical properties to various segmented organs, which is likely to result in inaccurate reconstructions. Furthermore, DOT based only on intensity (continuous wave-DOT) is a nonunique inverse problem, and hence, cannot be used to retrieve simultaneously maps of absorption and diffusion coefficients. We propose a method that reconstructs a single parameter from the excitation measurements, which is used in the fDOT problem to accurately recover fluorescence distribution.

A quantitative assessment of the depth sensitivity of an optical topography system using a solid dynamic tissue-phantom

A solid dynamic phantom with tissue-like optical properties is presented, which contains seven discrete targets impregnated with thermochromic pigment located at different depths from the surface. Changes in absorption are obtained in response to localized heating of the targets, simulating haemodynamic changes occurring in the brain and other tissues. The depth sensitivity of a continuous wave optical topography system was assessed successfully using the phantom. Images of the targets have been reconstructed using a spatially variant regularization, and the determined spatial localization in the depth direction is shown to be accurate within an uncertainty of about 3 mm down to a depth of about 30 mm.

Accelerated Optical Projection Tomography Applied to In Vivo Imaging of Zebrafish.

Optical projection tomography (OPT) provides a non-invasive 3-D imaging modality that can be applied to longitudinal studies of live disease models, including in zebrafish. Current limitations include the requirement of a minimum number of angular projections for reconstruction of reasonable OPT images using filtered back projection (FBP), which is typically several hundred, leading to acquisition times of several minutes. It is highly desirable to decrease the number of required angular projections to decrease both the total acquisition time and the light dose to the sample. This is particularly important to enable longitudinal studies, which involve measurements of the same fish at different time points. In this work, we demonstrate that the use of an iterative algorithm to reconstruct sparsely sampled OPT data sets can provide useful 3-D images with 50 or fewer projections, thereby significantly decreasing the minimum acquisition time and light dose while maintaining image quality. A transgenic zebrafish embryo with fluorescent labelling of the vasculature was imaged to acquire densely sampled (800 projections) and under-sampled data sets of transmitted and fluorescence projection images. The under-sampled OPT data sets were reconstructed using an iterative total variation-based image reconstruction algorithm and compared against FBP reconstructions of the densely sampled data sets. To illustrate the potential for quantitative analysis following rapid OPT data acquisition, a Hessian-based method was applied to automatically segment the reconstructed images to select the vasculature network. Results showed that 3-D images of the zebrafish embryo and its vasculature of sufficient visual quality for quantitative analysis can be reconstructed using the iterative algorithm from only 32 projections—achieving up to 28 times improvement in imaging speed and leading to total acquisition times of a few seconds.

Three-dimensional optical topography of brain activity in infants watching videos of human movement

We present 3D optical topography images reconstructed from data obtained previously while infants observed videos of adults making natural movements of their eyes and hands. The optical topography probe was placed over the temporal cortex, which in adults is responsible for cognitive processing of similar stimuli. Increases in oxyhaemoglobin were measured and reconstructed using a multispectral imaging algorithm with spatially variant regularization to optimize depth discrimination. The 3D optical topography images suggest that similar brain regions are activated in infants and adults. Images were presented showing the distribution of activation in a plane parallel to the surface, as well as changes in activation with depth. The time-course of activation was followed in the pixel which demonstrated the largest change, showing that changes could be measured with high temporal resolution. These results suggest that infants a few months old have regions which are specialized for reacting to human activity, and that these subtle changes can be effectively analysed using 3D optical topography.

Tomographic imaging with polarized light

We report three-dimensional tomographic reconstruction of optical parameters for the mesoscopic light scattering regime from experimentally obtained datasets by using polarized light. We present a numerically inexpensive approximation to the radiative transfer equation governing the polarized light transport. This approximation is employed in the reconstruction algorithm, which computes two optical parameters by using parallel and perpendicular polarizations of transmitted light. Datasets were obtained by imaging a scattering phantom embedding highly absorbing inclusions. Reconstruction results are presented and discussed.