In many medical imaging modalities, as photons travel from the emission source to the detector, they are scattered by the biological tissue. Often this scatter is viewed as a phenomenon that degrades image quality, and most research is focused on designing methods for either discarding the scattered photons or correcting for scatter. However, the scattered photons also carry information about the tissue that they pass through, which can perhaps be extracted. In this research, we investigate methods to retrieve information from the scattered photons in two specific medical imaging modalities: diffuse optical tomography (DOT) and single photon emission computed tomography (SPECT). To model the scattering of photons in biological tissue, we investigate using the Neumann-series form of the radiative transport equation (RTE). Since the scattering phenomenon are different in DOT and SPECT, the models are individually designed for each modality. In the DOT study, we use the developed photon-propagation model to investigate signal detectability in tissue. To study this detectability, we demonstrate the application of a surrogate figure of merit, based on Fisher information, which approximates the Bayesian ideal observer performance. In the SPECT study, our aim is to determine if only the SPECT emission data acquired in list-mode (LM) format, including the scattered-photon data, can be used to compute the tissue-attenuation map. We first propose a path-based formalism to process scattered photon data, and follow it with deriving expressions for the Fisher information that help determine the information content of LM data. We then derive a maximum-likelihood expectation-maximization algorithm that can jointly reconstruct the activity and attenuation map using LM SPECT emission data. While the DOT study can provide a boost in transition of DOT to clinical imaging, the SPECT study will provide insights on whether it is worth exposing the patient to extra X-ray radiation dose in order to obtain an attenuation map. Finally, although the RTE can be used to model light propagation in tissues, it is computationally intensive and therefore time consuming. To increase the speed of computation in the DOT study, we develop software to implement the RTE on parallel computing architectures, specifically the NVIDIA graphics processing units (GPUs).

This thesis reports the work done towards design and fabrication of a versatile and low cost, frequency domain DOT (Diffuse Optical Tomography) Imager. A design which uses only a single fiber for the source and a single fiber bundle for the detector is reported. From near the source, to diametrically opposite to the source, the detected intensity of scattered light varies by three to four orders in magnitude, depending on the tissue/phantom absorption and scattering properties. The photo multiplier tube’s (PMT’s) gain is controlled to operate it in the linear range, thus increasing the dynamic range of detection. Increasing the dynamic range by multi channel data acquisition is also presented. Arresting the oscillations of a stepper using a negative torque braking method is also adopted in this application for increasing the speed of data acquisition. The finite element method (FEM) for obtaining photon density solution to the transport equation and the model based iterative image reconstruction (MPBIIR) algorithm are developed for verifying the experimental prototype. Simulation studies presented towards the end of this thesis work provide insight into the nature of measurements. The optical absorption reconstructed images from the simulation, verified the validity of implementation of the reconstruction method for further reconstructions from data gathered from the developed imager. A single iteration of MOBIIR to segment the region of interest (ROI) using an homogeneous measurement estimate is presented. Using the single iteration MOBIIR to obtain a relatively more accurate starting value for the optical absorption coefficient, and the reconstruction results for data obtained from tissue mimicking solid epoxy-resin phantom with a single in-homogeneity inclusion is also presented to demonstrate the imager prototype.

Diffuse Optical Tomography is a diagnostic imaging modality where optical parameters such as absorption coefficient, scattering coefficient and refractive index distributions are recovered to form the internal tissue metabolic image. Near-infrared (NIR) light has the potential to be used as a noninvasive means of diagnostic imaging within the human breast. Due to the diffusive nature of light in tissue, computational model-based methods are required for functional imaging. The main goal is to recover the spatial variation of optical properties which shed light on the different metabolic states of tissue and tissue like media. This thesis addresses the issue of quantitative recovery of optical properties of tissue-mimicking phantom and pork tissue using diffuse optical tomography (DOT). The main contribution of the present work is the development of robust, efficient and fast optical property reconstruction algorithms for a direct 3-D DOT imaging system. There are both theoretical and experimental contributions towards the development of an imaging system and procedures to minimize accurate data collection time, overall system automation as well as development of computational algorithms. In nurturing the idea of imaging using NIR light into a fully developed direct 3-D imaging system, challenges from the theoretical and computational aspects have to be met. The recovery of the optical property distribution in the interior of the object from the often noisy boundary measurements on light, is an ill-posed ( and nonlinear) problem. This is particularly true, when one is interested in a direct 3-D image reconstruction instead of the often employed stacking of 2-D cross-sections obtained from solving a set of 2-D DOT problems. In order to render the DOT, a useful diagnostic imaging tool and a robust reconstruction procedure giving accurate and reliable parameter recovery in the scenario, where the number of unknowns far outnumbers the number of independent data sets that can be gathered (for example, the direct 3-D recovery mentioned earlier) is essential. Here, the inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. An interesting development in this direction has been the development of Broyden’ s and adjoint Broyden’ s methods that avoids direct Jacobian computation in each iteration thereby making the full 3-D a reality. Conventional model based iterative image reconstruction (MoBIIR) algorithm uses Newton’ s and it’s variant methods, where it required repeated evaluation of whole Jacobian, which consumes bulk time in reconstruction process. The explicit secant and adjoint information based fast 2-D/3-D image reconstruction algorithms without repeated evaluation of the Jacobian is proposed in diffuse optical tomography, where the computational time has been decreased many folds by updating the Jacobian successively through low rank update. An alternative route to the iterative solution is attempted by introducing an artificial dynamics in the system and treating the steady-state response of the artificially evolving dynamical system as a solution. The objective is to consider a novel family of pseudo-dynamical 2-D and 3-D systems whose numerical integration in time provides an asymptotic solution to the inverse problem at hand. We convert Gauss-Newton’ s equation for updates into a pseudo-dynamical (PD) form by explicitly adding a time derivative term. As the pseudo-time integration schemes do not need such explicit matrix inversion and depending on the pseudo-time step size, provides for a layer of regularization that in turn helps in superior quality of 2-D and 3-D image reconstruction. A cost effective frequency domain Matlab based 2-D/3-D automated imaging system is designed and built. The complete instrumentation (including PC-based control software) has been developed using a single modulated laser source (wavelength 830nm) and a photo-multiplier tube (PMT). The source and detector fiber change their positions dynamically allowing us to gather data at multiple source and detector locations. The fiber positions are adjusted on the phantom surface automatically for scanning variable size phantoms. A heterodyning scheme was used for reading out the measurement using a lock-in-amplifier. The Matlab program carries out sequence of actions such as instrument control, data acquisition, data organization, data calibration and reconstruction of image. The Gauss-Newton’ s, Broyden’ s, adjoint Broyden’ s and pseudo-time integration algorithms are evaluated using the simulation data as well as data from the experimental DOT system. Validation of the system and the reconstruction algorithms were carried out on a real tissue, a pork tissue with an embedded fat inhomogeneity. The results were found to match the known parameters closely.

Stable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation, namely, diffuse optical tomography (DOT) and one of its variations, ultrasound-modulated optical tomography (UMOT). Since in both these imaging modalities the system matrices are ill-conditioned owing to insufficient and noisy data, the emphasis in this work is to develop robust stochastic filtering algorithms which can handle measurement noise and also account for inaccuracies in forward models through an appropriate assignment of a process noise. However, we start with demonstration of speeding of a Gauss-Newton (GN) algorithm for DOT so that a video-rate reconstruction from data recorded on a CCD camera is rendered feasible. Towards this, a computationally efficient linear iterative scheme is proposed to invert the normal equation of a Gauss-Newton scheme in the context of recovery of absorption coefficient distribution from DOT data, which involved the singular value decomposition (SVD) of the Jacobian matrix appearing in the update equation. This has sufficiently speeded up the inversion that a video rate recovery of time evolving absorption coefficient distribution is demonstrated from experimental data. The SVD-based algorithm has made the number of operations in image reconstruction to be rather than. 2()ONN3()ONN The rest of the algorithms are based on different forms of stochastic filtering wherein we arrive at a mean-square estimate of the parameters through computing their joint probability distributions conditioned on the measurement up to the current instant. Under this, the first algorithm developed uses a Bootstrap particle filter which also uses a quasi-Newton direction within. Since keeping track of the Newton direction necessitates repetitive computation of the Jacobian, for all particle locations and for all time steps, to make the recovery computationally feasible, we devised a faster update of the Jacobian. It is demonstrated, through analytical reasoning and numerical simulations, that the proposed scheme, not only accelerates convergence but also yields substantially reduced sample variance in the estimates vis-à-vis the conventional BS filter. Both accelerated convergence and reduced sample variance in the estimates are demonstrated in DOT optical parameter recovery using simulated and experimental data. In the next demonstration a derivative free variant of the pseudo-dynamic ensemble Kalman filter (PD-EnKF) is developed for DOT wherein the size of the unknown parameter is reduced by representing of the inhomogeneities through simple geometrical shapes. Also the optical parameter fields within the inhomogeneities are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions). The EnKF is then used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the Pseudo-Dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ‘measurement’ equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. In our numerical simulations we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes ( such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as = 0.01 mm-1 and = 1.0 mm-1respectively. We also assume=0.02 mm-1 within the inhomogeneity (for the single inhomogeneity case) and=0.02 and 0.03 mm-1 (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. The superiority of a modified version of the PD-EnKF, which uses an ensemble square root filter, is also demonstrated in the context of UMOT by recovering the distribution of mean-squared amplitude of vibration, related to the Young’s modulus, in the ultrasound focal volume. Since the ability of a coherent light probe to pick-up the overall optical path-length change is limited to modulo an optical wavelength, the individual displacements suffered owing to the US forcing should be very small, say within a few angstroms. The sensitivity of modulation depth to changes in these small displacements could be very small, especially when the ROI is far removed from the source and detector. The contrast recovery of the unknown distribution in such cases could be seriously impaired whilst using a quasi-Newton scheme (e.g. the GN scheme) which crucially makes use of the derivative information. The derivative-free gain-based Monte Carlo filter not only remedies this deficiency, but also provides a regularization insensitive and computationally competitive alternative to the GN scheme. The inherent ability of a stochastic filter in accommodating the model error owing to a diffusion approximation of the correlation transport may be cited as an added advantage in the context of the UMOT inverse problem. Finally to speed up forward solve of the partial differential equation (PDE) modeling photon transport in the context of UMOT for which the PDE has time as a parameter, a spectral decomposition of the PDE operator is demonstrated. This allows the computation of the time dependent forward solution in terms of the eigen functions of the PDE operator which has speeded up the forward solution, which in turn has rendered the UMOT parameter recovery computationally efficient.