Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and unstructured geometries, non-linearity of the data fitting and regularization terms, and non-differentiability of the regularization term. We develop several approaches to overcome these difficulties by: i) defining discrete differential operators for unstructured geometries using both finite element and graph representations; ii) developing an optimization algorithm based on the alternating direction method of multipliers (ADMM) for the non-differentiable and non-linear minimization problem; iii) investigating isotropic and anisotropic variants of TV regularization, and comparing their finite element- and graph-based implementations. These approaches are evaluated on experiments on simulated data and real data acquired from a tissue phantom. Our results show that both FEM and graph-based TV regularization is able to accurately reconstruct both sparse and non-sparse distributions without the over-smoothing effect of Tikhonov regularization and the over-sparsifying effect of L$_1$ regularization. The graph representation was found to out-perform the FEM method for low-resolution meshes, and the FEM method was found to be more accurate for high-resolution meshes.Comment: 24 pages, 11 figures. Reviced version includes revised figures and improved clarit

Sparsity-Driven Reconstruction for FDOT With Anatomical Priors

In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical regions where the fluorescent probe has accumulated, and second, a regularization effect inside the selected anatomical regions. After formulating the reconstruction in a variational framework, we analyze the resulting optimization problem and derive a practical numerical method tailored to (2, 1)-mixed-norm regularization. The proposed method includes as particular cases other sparsity promoting regularization methods such as -norm penalization and total variation penalization. Results on synthetic and experimental data are presented

Estudios sobre la tomografía óptica difusiva de fluorescencia

La Tomografía Óptica Difusiva de Fluorescencia (FDOT) es una técnica de imagen molecular de reciente creación, que ha atraído fuertemente la atención de la comunidad de investigadores biomédicos “preclínicos”, pues utiliza radiación no ionizante y su coste es muy bajo. La conjunción de estos factores la perfilan como una alternativa posible al paradigma nuclear en la investigación con animales pequeños. Debido a la juventud de la técnica, se plantean numerosos interrogantes que abarcan desde sus áreas de aplicación al discurrir de su desarrollo tecnológico. Es la intención de este trabajo dar respuesta a algunos de ellos. En lo que concierne al desarrollo tecnológico hemos construido un FDOT de geometría de placas paralelas que utiliza un reconstructor optimizado. Posteriormente el sistema ha sido clonado, incluyéndose en el gantry rotatorio de un tomógrafo de rayos X (CT). Usando estos dispositivos hemos querido resolver dos cuestiones técnicas relevantes: la primera relativa al grado de detalle necesario en el modelo matemático de transporte de luz. Este modelo alimenta el algoritmo de reconstrucción y habitualmente se construye suponiendo que los sujetos tienen propiedades ópticas homogéneas, junto con el uso de datos normalizados. Hemos demostrado que esta asunción no es válida en presencia de heterogeneidades de dispersión. La segunda cuestión hace referencia a la geometría del montaje experimental, demostrando que la adquisición en placas paralelas es capaz de proporcionar reconstrucciones de mejor calidad que la adquisición en rotación. En lo referente a las áreas de aplicación, en este documento demostramos la capacidad de la técnica para cuantificar in-vivo la concentración de células T fluorescentes en los ganglios cervicales y en el timo de ratones transgénicos

Multiplexed fluorescence diffuse optical tomography

Fluorescence tomography (FT) is an emerging non-invasive in vivo molecular imaging modality that aims at quantification and three-dimensional (3D) localization of fluorescent tagged inclusions, such as cancer lesions and drug molecules, buried deep in human and animal subjects. Depth-resolved 3D reconstruction of fluorescent inclusions distributed over the volume of optically turbid biological tissue using the diffuse fluorescent photons detected on the skin poses a highly ill-conditioned problem, as depth information must be extracted from boundary data. Due to this ill-posed nature of FT reconstructions, noise and errors in the data can severely impair the accuracy of the 3D reconstructions. Consequently, improvements in the signal-to-noise ratio (SNR) of the data significantly enhance the quality of the FT reconstructions. Furthermore, enhancing the SNR of the FT data can greatly contribute to the speed of FT scans. The pivotal factor in the SNR of the FT data is the power of the radiation illuminating the subject and exciting the administered fluorescent agents. In existing single-point illumination FT systems, the illumination power level is limited by the skin maximum radiation exposure levels. In this research, a multiplexed architecture governed by the Hadamard transform was conceptualized, developed, and experimentally implemented for orders-of-magnitude enhancement of the SNR and the robustness of FT reconstructions. The multiplexed FT system allows for Hadamard-coded multi-point illumination of the subject while maintaining the maximal information content of the FT data. The significant improvements offered by the multiplexed FT system were validated by numerical and experimental studies carried out using a custom-built multiplexed FT system developed exclusively in this work. The studies indicate that Hadamard multiplexing offers significantly enhanced robustness in reconstructing deep fluorescent inclusions from low-SNR FT data.Ph.D

Improved Modeling and Image Generation for Fluorescence Molecular Tomography (FMT) and Positron Emission Tomography (PET)

In this thesis, we aim to improve quantitative medical imaging with advanced image generation algorithms. We focus on two specific imaging modalities: fluorescence molecular tomography (FMT) and positron emission tomography (PET). For FMT, we present a novel photon propagation model for its forward model, and in addition, we propose and investigate a reconstruction algorithm for its inverse problem. In the first part, we develop a novel Neumann-series-based radiative transfer equation (RTE) that incorporates reflection boundary conditions in the model. In addition, we propose a novel reconstruction technique for diffuse optical imaging that incorporates this Neumann-series-based RTE as forward model. The proposed model is assessed using a simulated 3D diffuse optical imaging setup, and the results demonstrate the importance of considering photon reflection at boundaries when performing photon propagation modeling. In the second part, we propose a statistical reconstruction algorithm for FMT. The algorithm is based on sparsity-initialized maximum-likelihood expectation maximization (MLEM), taking into account the Poisson nature of data in FMT and the sparse nature of images. The proposed method is compared with a pure sparse reconstruction method as well as a uniform-initialized MLEM reconstruction method. Results indicate the proposed method is more robust to noise and shows improved qualitative and quantitative performance. For PET, we present an MRI-guided partial volume correction algorithm for brain imaging, aiming to recover qualitative and quantitative loss due to the limited resolution of PET system, while keeping image noise at a low level. The proposed method is based on an iterative deconvolution model with regularization using parallel level sets. A non-smooth optimization algorithm is developed so that the proposed method can be feasibly applied for 3D images and avoid additional blurring caused by conventional smooth optimization process. We evaluate the proposed method using both simulation data and in vivo human data collected from the Baltimore Longitudinal Study of Aging (BLSA). Our proposed method is shown to generate images with reduced noise and improved structure details, as well as increased number of statistically significant voxels in study of aging. Results demonstrate our method has promise to provide superior performance in clinical imaging scenarios

Contributions to the improvement of image quality in CBCT and CBμCT and application in the development of a CBμCT system

During the last years cone-beam x-ray CT (CBCT) has been established as a widespread imaging technique and a feasible alternative to conventional CT for dedicated imaging tasks for which the limited flexibility offered by conventional CT advises the development of dedicated designs. CBCT systems are starting to be routinely used in image guided radiotherapy; image guided surgery using C-arms; scan of body parts such as the sinuses, the breast or extremities; and, especially, in preclinical small-animal imaging, often coupled to molecular imaging systems. Despite the research efforts advocated to the advance of CBCT, the challenges introduced by the use of large cone angles and two-dimensional detectors are a field of vigorous research towards the improvement of CBCT image quality. Moreover, systems for small-animal imaging add to the challenges posed by clinical CBCT the need of higher resolution to obtain equivalent image quality in much smaller subjects. This thesis contributes to the progress of CBCT imaging by addressing a variety of issues affecting image quality in CBCT in general and in CBCT for small-animal imaging (CBμCT). As part of this work we have assessed and optimized the performance of CBμCT systems for different imaging tasks. To this end, we have developed a new CBμCT system with variable geometry and all the required software tools for acquisition, calibration and reconstruction. The system served as a tool for the optimization of the imaging process and for the study of image degradation effects in CBμCT, as well as a platform for biological research using small animals. The set of tools for the accurate study of CBCT was completed by developing a fast Monte Carlo simulation engine based on GPUs, specifically devoted to the realistic estimation of scatter and its effects on image quality in arbitrary CBCT configurations, with arbitrary spectra, detector response, and antiscatter grids. This new Monte Carlo engine outperformed current simulation platforms by more than an order of magnitude. Due to the limited options for simulation of spectra in microfocus x-ray sources used in CBμCT, we contributed in this thesis a new spectra generation model based on an empirical model for conventional radiology and mammography sources modified in accordance to experimental data. The new spectral model showed good agreement with experimental exposure and attenuation data for different materials. The developed tools for CBμCT research were used for the study of detector performance in terms of dynamic range. The dynamic range of the detector was characterized together with its effect on image quality. As a result, a new simple method for the extension of the dynamic range of flat-panel detectors was proposed and evaluated. The method is based on a modified acquisition process and a mathematical treatment of the acquired data. Scatter is usually identified as one of the major causes of image quality degradation in CBCT. For this reason the developed Monte Carlo engine was applied to the in-depth study of the effects of scatter for a representative range of CBCT embodiments used in the clinical and preclinical practice. We estimated the amount and spatial distribution of the total scatter fluence and the individual components within. The effect of antiscatter grids in improving image quality and in noise was also evaluated. We found a close relation between scatter and the air gap of the system, in line with previous results in the literature. We also observed a non-negligible contribution of forward-directed scatter that is responsible to a great extent for streak artifacts in CBCT. The spatial distribution of scatter was significantly affected by forward scatter, somewhat challenging the usual assumption that the scatter distribution mostly contains low-frequencies. Antiscatter grids showed to be effective for the reduction of cupping, but they showed a much lower performance when dealing with streaks and a shift toward high frequencies of the scatter distributions. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------A lo largo de los últimos años, el TAC de rayos X de haz cónico (CBCT, de “conebeam” CT) se ha posicionado como una de las técnicas de imagen más ampliamente usadas. El CBCT se ha convertido en una alternativa factible al TAC convencional en tareas de imagen específicas para las que la flexibilidad limitada ofrecida por este hace recomendable el desarrollo de sistemas de imagen dedicados. De esta forma, el CBCT está empezando a usarse de forma rutinaria en varios campos entre los que se incluyen la radioterapia guiada por imagen, la cirugía guiada por imagen usando arcos en C, imagen de partes de la anatomía en las que el TAC convencional no es apropiado, como los senos nasales, las extremidades o la mama, y, especialmente el campo de imagen preclínica con pequeño animal. Los sistemas CBCT usados en este último campo se encuentran habitualmente combinados con sistemas de imagen molecular. A pesar del trabajo de investigación dedicado al avance de la técnica CBCT en los últimos años, los retos introducidos por el uso de haces cónicos y de detectores bidimensionales son un campo candente para la investigación médica, con el objetivo de obtener una calidad de imagen equivalente o superior a la proporcionada por el TAC convencional. En el caso de imagen preclínica, a los retos generados por el uso de CBCT se une la necesidad de una mayor resolución de imagen que permita observar estructuras anatómicas con el mismo nivel de detalle obtenido para humanos. Esta tesis contribuye al progreso del CBCT mediante el estudio de usa serie de efectos que afectan a la calidad de imagen de CBCT en general y en el ámbito preclínico en particular. Como parte de este trabajo, hemos evaluado y optimizado el rendimiento de sistemas CBCT preclínicos en función de la tarea de imagen concreta. Con este fin se ha desarrollado un sistema CBCT para pequeños animales con geometría variable y todas las herramientas necesarias para la adquisición, calibración y reconstrucción de imagen. El sistema sirve como base para la optimización de protocolos de adquisición y para el estudio de fuentes de degradación de imagen además de constituir una plataforma para la investigación biológica en pequeño animal. El conjunto de herramientas para el estudio del CBCT se completó con el desarrollo de una plataforma acelerada de simulación Monte Carlo basada en GPUs, optimizada para la estimación de radiación dispersa en CBCT y sus efectos en la calidad de imagen. La plataforma desarrollada supera el rendimiento de las actuales en más de un orden de magnitud y permite la inclusión de espectros policromáticos de rayos X, de la respuesta realista del detector y de rejillas antiscatter. Debido a las escasas opciones ofrecidas por la literatura para la estimación de espectros de rayos X para fuentes microfoco usadas en imagen preclínica, en esta tesis se incluye el desarrollo de un nuevo modelo de generación de espectros, basado en un modelo existente para fuentes usadas en radiología y mamografía. El modelo fue modificado a partir de datos experimentales. La precisión del modelo presentado se comprobó mediante datos experimentales de exposición y atenuación para varios materiales. Las herramientas desarrolladas se usaron para estudiar el rendimiento de detectores de rayos tipo flat-panel en términos de rango dinámico, explorando los límites impuestos por el mismo en la calidad de imagen. Como resultado se propuso y evaluó un método para la extensión del rango dinámico de este tipo de detectores. El método se basa en la modificación del proceso de adquisición de imagen y en una etapa de postproceso de los datos adquiridos. El simulador Monte Carlo se empleó para el estudio detallado de la naturaleza, distribución espacial y efectos de la radiación dispersa en un rango de sistemas CBCT que cubre el espectro de aplicaciones propuestas en el entorno clínico y preclínico. Durante el estudio se inspeccionó la cantidad y distribución espacial de radiación dispersa y de sus componentes individuales y el efecto causado por la inclusión de rejillas antiscatter en términos de mejora de calidad de imagen y de ruido en la imagen. La distribución de radiación dispersa mostró una acentuada relación con la distancia entre muestra y detector en el equipo, en línea con resultados publicados previamente por otros autores. También se encontró una influencia no despreciable de componentes de radiación dispersa con bajos ángulos de desviación, poniendo en tela de juicio la tradicional asunción que considera que la distribución espacial de la radiación dispersa está formada casi exclusivamente por componentes de muy baja frecuencia. Las rejillas antiscatter demostraron ser efectivas para la reducción del artefacto de cupping, pero su efectividad para tratar artefactos en forma de línea (principalmente formados por radiación dispersa con bajo ángulo de desviación) resultó mucho menor. La inclusión de estas rejillas también enfatiza las componentes de alta frecuencia de la distribución espacial de la radiación dispersa