Effective optode configuration for the image reconstruction in diffuse optical tomography

We describe a method to increase the speed of convergence for the simultaneous reconstruction of absorption and scattering images in Diffuse Optical Tomography (DOT). We used the diffusion approximation of the radiative transfer equation and the Finite Element Method (FEM) to solve the forward problem. The absorption and reduced scattering images are reconstructed by inverting the distribution of the moments of the time-dependent detected light flux. The inverse problem is solved with an optimization algorithm like ART or Conjugate Gradient. This ill-posed inverse problem can be simplified by using <i>a priori</i> knowledge of the studied objects. In this paper, we consider that DOT is a functional imaging technique that can be complemented by an anatomical imaging technique like Magnetic Resonance Imaging (MRI). We used anatomic information obtained from MRI as prior knowledge to compute optical absorption and scattering images. In a first step, MRI segmented images were only used to mesh our phantoms, with a finer resolution around boundaries. In a second step, we computed optical images with homogeneous properties from the segmented MRI image, in order to initialise our optimisation process. These two initialisations yield better reconstructed images. Reconstruction from simulated and experimental data will be presented.

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

We describe a method to increase the speed of convergence for the simultaneous reconstruction of absorption and scattering images in Diffuse Optical Tomography (DOT). We used the diffusion approximation of the radiative transfer equation and the Finite Element Method (FEM) to solve the forward problem. The absorption and reduced scattering images are reconstructed by inverting the distribution of the moments of the time-dependent detected light flux. The inverse problem is solved with an optimization algorithm like ART or Conjugate Gradient. This ill-posed inverse problem can be simplified by using a priori knowledge of the studied objects. In this paper, we consider that DOT is a functional imaging technique that can be complemented by an anatomical imaging technique like Magnetic Resonance Imaging (MRI). We used anatomic information obtained from MRI as prior knowledge to compute optical absorption and scattering images. In a first step, MRI segmented images were only used to mesh our phantoms, with a finer resolution around boundaries. In a second step, we computed optical images with homogeneous properties from the segmented MRI image, in order to initialise our optimisation process. These two initialisations yield better reconstructed images. Reconstruction from simulated and experimental data will be presented.

The underdeterminedness of the inverse problems encountered in diffuse optical tomography (DOT) becomes especially severe when detecting breast cancers, because much more variables are needed to be reconstructed due to the big-size. With the addition of ill-condition caused by the diffusive nature of light propagation, the ill-posedness makes it very difficult to improve the image reconstruction. Fortunately, from the anatomy viewpoint, we have known that the cancer is distributed locally and only amounts to a small percentage of the whole breast. This makes it possible to employ the compressive sensing theory to mitigate the ill-posedness, based on the prior knowledge about the sparsity of the signal to be reconstructed. Specifically speaking, sparsity regularizations can be used in DOT to improve the image reconstruction under the premise that un-increase the number of measurements required in the reconstruction. In this paper, we primarily focus on comparing the performances of different kinds of L_p-norm-based regularizations in terms of theory and real effects, respectively. The numerical and phantom experiments have proven that the sparsity regularizations can dramatically improve the image reconstruction. Furthermore, as the p in the L_p-norm decreasing to zero, the solutions become sparser and the corresponding image quality gets higher, with smooth L₀-norm-based regularization providing the highest image quality.

In diffuse optical tomography (DOT), real-time image reconstruction of oxy- and deoxy-haemoglobin changes occurring in the brain could give valuable information in clinical care settings. Although non-linear reconstruction techniques could provide more accurate results, their computational burden makes them unsuitable for real-time applications. Linear techniques can be employed under the assumption that the expected change in absorption is small. Several approaches exist, differing primarily in their handling of regularization and the noise statistics. In real experiments, it is impossible to compute the true noise statistics, because of the presence of physiological oscillations in the measured data. This is even more critical in real-time applications, where no off-line filtering and averaging can be performed to reduce the noise level. Therefore, many studies substitute the noise covariance matrix with the identity matrix. In this paper, we examined two questions: does using the noise model with realistic, imperfect data yield an improvement in image quality compared to using the identity matrix; and what is the difference in quality between online and offline reconstructions. Bespoke test data were created using a novel process through which simulated changes in absorption were added to real resting-state DOT data. A realistic multi-layer head model was used as the geometry for the reconstruction. Results validated our assumptions, highlighting the validity of computing the noise statistics from the measured data for online image reconstruction, which was performed at 2 Hz. Our results can be directly extended to a real application where real-time imaging is required.

The relationship between conventional reference measurement correction and approximation error modelling in linear reconstruction in diffuse optical tomography is considered.

We present high spatial density, multi-modal, parallel-plate Diffuse Optical Tomography (DOT) imaging systems for the purpose of breast tumor detection. One hybrid instrument provides time domain (TD) and continuous wave (CW) DOT at 64 source fiber positions. The TD diffuse optical spectroscopy with PMT- detection produces low-resolution images of absolute tissue scattering and absorption while the spatially dense array of CCD-coupled detector fibers (108 detectors) provides higher-resolution CW images of relative tissue optical properties. Reconstruction of the tissue optical properties, along with total hemoglobin concentration and tissue oxygen saturation, is performed using the TOAST software suite. Comparison of the spatially-dense DOT images and MR images allows for a robust validation of DOT against an accepted clinical modality. Additionally, the structural information from co-registered MR images is used as a spatial prior to improve the quality of the functional optical images and provide more accurate quantification of the optical and hemodynamic properties of tumors. We also present an optical-only imaging system that provides frequency domain (FD) DOT at 209 source positions with full CCD detection and incorporates optical fringe projection profilometry to determine the breast boundary. This profilometry serves as a spatial constraint, improving the quality of the DOT reconstructions while retaining the benefits of an optical-only device. We present initial images from both human subjects and phantoms to display the utility of high spatial density data and multi-modal information in DOT reconstruction with the two systems.

Malignant breast lesions manifest in a variety of shapes and configurations. Here we propose an algorithm utilizing anisotropic-tumor-prior guided diffuse optical tomography (DOT) reconstructions to recover an unknown tumor’s orientation and shape anisotropy.

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.

Through application of spatio-temporal regularisation techniques, we demonstrate the real-time three-dimensional dynamic reconstruction of the optical properties of a hemispherical infant head phantom, with moving absorption and scattering targets.

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

This paper introduces an improved diffusion model which is accurate and fast in computation for the cases of mu(a)/mu'(s) < 0.07 as good as the conventional diffusion model for the cases of mu(a)/mu'(s) < 0.007 for surface measurement, hence more suitable than the conventional model to be the forward model used in the image reconstruction in the diffuse optical tomography. Deviation of the diffusion approximation (DA) on the medium surface is first studied in the Monte Carlo (MC) diffusion hybrid model for reflectance setup. A modification of DA and an improved MC diffusion hybrid model based on this modified DA are introduced. Numerical tests show that for media with relatively strong absorption the present modified diffusion approach can reduce the surface deviation significantly in both the hybrid and pure diffusion model, and consumes nearly no more computation time than the conventional diffusion approach.

We attempt to develop a systematic scheme through adopting high-pass filtering (HPF) to well resolve value-preserved images such as medical images. Our approach is derived from the Poisson maximum a posteriori superresolution algorithm employing the HP filters, where four filters are considered such as two low-pass-filter-combination based filters, wavelet filter, and negative-oriented Laplacian HP filter. The proposed approach is incorporated into the procedure of finite-element-method (FEM)-based image reconstruction for diffuse optical tomography in the direct current domain, posterior to each iteration without altering the original FEM modeling. This approach is justified with various HPF for different cases that breast-like phantoms embedded with two or three inclusions that imitate tumors are employed to examine the resolution performances under certain extreme conditions. The proposed approach to enhancing image resolution is evaluated for all tested cases. A qualitative investigation of reconstruction performance for each case is presented. Following this, we define a set of measures on the quantitative evaluation for a range of resolutions including separation, size, contrast, and location, thereby providing a comparable evaluation to the visual quality. The most satisfactory result is obtained by using the wavelet HP filter, and it successfully justifies our proposed scheme.

Fluorescence diffuse optical tomography (fDOT) is a noninvasive imaging technique that makes it possible to quantify the spatial distribution of fluorescent tracers in small animals. fDOT image reconstruction is commonly performed by means of iterative methods such as the algebraic reconstruction technique (ART). The useful results yielded by more advanced l1-regularized techniques for signal recovery and image reconstruction, together with the recent publication of Split Bregman (SB) procedure, led us to propose a new approach to the fDOT inverse problem, namely, ART-SB. This method alternates a cost-efficient reconstruction step (ART iteration) with a denoising filtering step based on minimization of total variation of the image using the SB method, which can be solved efficiently and quickly. We applied this method to simulated and experimental fDOT data and found that ART-SB provides substantial benefits over conventional ART.

The adaptive finite element method (AFEM) is an effective way to retain enough resolution in selected regions while improving computational efficiency for reconstruction in fluorescent molecular tomography (FMT). In addition, background optical properties acquired by diffuse optical tomography (DOT) will improve the quality of reconstructed images. In this work, a DOT-guided adaptive reconstruction method (DGARM) is proposed, in which DOT is introduced into an adaptive reconstruction framework of FMT. Besides being used as functional a priori information in the forward modeling, the reconstructed local absorption coefficients in DOT are also used to form internal structural a priori information, which is further used to identify regions of interest (ROIs) in the mesh refinement of the adaptive procedure. Because optical properties are recovered before the formulation of FMT, a linear relationship is established between the fluorescent field and boundary measurements. We implemented numerical simulations and physical experiments to evaluate the performance of the algorithm. Compared with the strategies of uniform meshing with DOT and AFEM without DOT, DGAM improves localization accuracy of the reconstruction of fluorescence inclusion.