Information theoretic regularization in diffuse optical tomography

Diffuse optical tomography (DOT) retrieves the spatially distributed optical characteristics of a medium from external measurements. Recovering these parameters of interest involves solving a non-linear and severely ill-posed inverse problem. In this thesis we propose methods towards the regularization of DOT via the introduction of spatially unregistered, a priori information from alternative high resolution anatomical modalities, using the information theory concepts of joint entropy (JE) and mutual information (MI). Such functionals evaluate the similarity between the reconstructed optical image and the prior image, while bypassing the multi-modality barrier manifested as the incommensurate relation between the gray value representations of corresponding anatomical features in the modalities involved. By introducing structural a priori information in the image reconstruction process, we aim to improve the spatial resolution and quantitative accuracy of the solution. A further condition for the accurate incorporation of a priori information is the establishment of correct alignment between the prior image and the probed anatomy in a common coordinate system. However, limited information regarding the probed anatomy is known prior to the reconstruction process. In this work we explore the potentiality of spatially registering the prior image simultaneously with the solution of the reconstruction process. We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results obtained by numerical simulations as well as experimental data. In addition we compare the performance of MI and JE. Finally, we propose a method for fast joint entropy evaluation and optimization, which we later employ for the information theoretic regularization of DOT. The main areas involved in this thesis are: inverse problems, image reconstruction & regularization, diffuse optical tomography and medical image registration

Digital Image Processing Applications

Digital image processing can refer to a wide variety of techniques, concepts, and applications of different types of processing for different purposes. This book provides examples of digital image processing applications and presents recent research on processing concepts and techniques. Chapters cover such topics as image processing in medical physics, binarization, video processing, and more

A Multivariate Approach to Functional Neuro Modeling

This Ph.D. thesis, A Multivariate Approach to Functional Neuro Modeling, deals with the analysis and modeling of data from functional neuro imaging experiments. A multivariate dataset description is provided which facilitates efficient representation of typical datasets and, more importantly, provides the basis for a generalization theoretical framework relating model performance to model complexity and dataset size. Briefly summarized the major topics discussed in the thesis include: ffl An introduction of the representation of functional datasets by pairs of neuronal activity patterns and overall conditions governing the functional experiment, via associated micro- and macroscopic variables. The description facilitates an efficient microscopic re-representation, as well as a handle on the link between brain and behavior; the latter is obtained by hypothesizing variations in the micro- and macroscopic variables to be manifestations of an underlying system. ffl A review of two micros..

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

Reduction of Limited Angle Artifacts in Medical Tomography via Image Reconstruction

Artifacts are unwanted effects in tomographic images that do not reflect the nature of the object. Their widespread occurrence makes their reduction and if possible removal an important subject in the development of tomographic image reconstruction algorithms. Limited angle artifacts are caused by the limited angular measurements, constraining the available tomographic information. This thesis focuses on reducing these artifacts via image reconstruction in two cases of incomplete measurements from: (1) the gaps left after the removal of high density objects such as dental fillings, screws and implants in computed tomography (CT) and (2) partial ring scanner configurations in positron emission tomography (PET). In order to include knowledge about the measurement and noise, prior terms were used within the reconstruction methods. Careful consideration was given to the trade-off between image blurring and noise reduction upon reconstruction of low-dose measurements.Development of reconstruction methods is an incremental process starting with testing on simple phantoms towards more clinically relevant ones by modeling the respective physical processes involved. In this work, phantoms were constructed to ensure that the proposed reconstruction methods addressed to the limited angle problem. The reconstructed images were assessed qualitatively and quantitatively in terms of noise reduction, edge sharpness and contrast recovery.Maximum a posteriori (MAP) estimation with median root prior (MRP) was selected for the reconstruction of limited angle measurements. MAP with MRP successfully reduced the artifacts caused by limited angle data in various datasets, tested with the reconstruction of both list-mode and projection data. In all cases, its performance was found to be superior to conventional reconstruction methods such as total-variation (TV) prior, maximum likelihood expectation maximization (MLEM) and filtered backprojection (FBP). MAP with MRP was also more robust with respect to parameter selection than MAP with TV prior.This thesis demonstrates the wide-range applicability of MAP with MRP in medical tomography, especially in low-dose imaging. Furthermore, we emphasize the importance of developing and testing reconstruction methods with application-specific phantoms, together with the properties and limitations of the measurements in mind

4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference

Bayesian inference in seismic tomography

In a variety of scientific applications we require methods to construct three dimensional maps of properties of the interior of solid media, and in the geosciences the medium is usually the Earth's subsurface. For each such map we need the corresponding map of uncertainties in those properties in order to assess their reliability. Seismic tomography is such a method which has been used widely to study properties of the subsurface of the Earth, for example, using surface wave dispersion data. Surface wave tomography is usually conducted using a two-step method by first estimating two-dimensional (2D) surface wave phase or group velocity maps at a series of frequencies and then inverting those for the 3D spatial velocity structure through a set of 1D inversions for structure with depth beneath each geographical location. Since surface wave tomography is a highly non-linear problem, it is usually solved using Monte Carlo (MC) sampling methods. However, since the 1D inversions in the second step are usually performed independently, lateral spatial correlations of the Earth can be lost. We therefore introduce a one-step MC method which inverts for a 3D velocity structure directly from frequency-dependent surface wave travel time measurements by using a fully 3D parametrization. The method was first applied to a synthetic test and compared with two-step linearised and two-step MC methods. The results show that by including lateral spatial correlations in the inversion the new method estimates velocity models and associated uncertainty significantly better in the sense that it produces more intuitively reasonable and interpretable results, and the computation cost is also comparable to the two-step MC method. We apply the 3D MC surface wave tomography method to a real dataset recorded using a dense passive seismic array installed on the North Sea seabed. The ambient noise data of each receiver pair are cross correlated to extract Scholte waves, in which two Scholte wave modes are observed. We separated the two modes using a dispersion compensation method. For each separated mode phase velocity maps are determined using Eikonal tomography. Those phase velocity maps are then used to estimate 3D shear velocities of the subsurface. To further understand the limitation of the approach, we conducted three different inversions: the usual 1D depth inversions, a 2D inversion along a 2D cross section and a fully 3D inversion. With each inversion the shear velocity structure is extracted along the same cross section and compared. The results confirm that 1D inversions can produce errors due to independence of those inversions, whereas 2D and 3D methods improve the results by including lateral spatial correlations in the inversion. The 3D results better match an existing shear velocity model obtained from active source seismic reflection tomography. This is probably because the 3D method uses frequency-dependent measurements directly, which naturally avoids errors introduced in the first 2D Eikonal tomography step. The results show a clear low velocity river channel, and exhibit another low velocity anomaly both in the phase velocity maps at short periods ( < 1.6 s) of the fundamental mode and in the shear-velocity model in the near surface ( < 250 m). The latter anomaly is correlated with the distribution of seabed pockmarks, indicating that the anomaly might be related to the circulation of near surface fluids. Apart from surface waves, seismological body wave travel times have also been used to study the Earth's interior and to characterize earthquakes. Body waves are generally sensitive to structure around the sub-volume in which earthquakes occur and produce limited sensitivity in the near surface, whereas surface waves are more sensitive to the shallower structure. Thus body waves and surface waves can be used jointly to better constrain the subsurface structure. Since the tomographic problem is usually highly non-linear, we apply MC sampling methods to invert for source parameters and velocity models simultaneously using earthquake body wave travel times and ambient noise surface wave dispersion data. The method is applied to a mining site in the U.K. where induced seismicity is recorded using a small local network and ambient noise data are available from the same stations. The results show that by using both types of data, earthquake source parameters and velocity models can be better constrained than in independent inversions. Synthetic tests show that the independent inversion using only body wave travel times can cause biases in the results due to trade-offs between source parameters and velocity models, while this issue can be largely resolved using joint inversion, indicating that the ambient noise data can provide additional information. Although MC sampling methods have been used widely to solve seismic tomographic problems, they are computationally expensive and remain intractable for large dataset problems. We therefore introduce variational inference methods to solve seismic tomographic problems. Variational inference solves the Bayesian inference problem using optimization, yet still provide probabilistic results. In this thesis we introduce two variational methods: automatic differential variational inference (ADVI) and Stein variational gradient descent (SVGD), and apply them to 2D seismic tomographic problems using both synthetic and real data. We compare the results with those obtained using two different MC sampling methods, and demonstrate that variational inference methods can provide accurate approximations to the results of MC sampling methods at significantly lower computational cost, provided that the gradient of model parameters with respect to data can be computed efficiently

Heterogeneidad tumoral en imágenes PET-CT

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Estructura de la Materia, Física Térmica y Electrónica, leída el 28/01/2021Cancer is a leading cause of morbidity and mortality [1]. The most frequent cancers worldwide are non–small cell lung carcinoma (NSCLC) and breast cancer [2], being their management a challenging task [3]. Tumor diagnosis is usually made through biopsy [4]. However, medical imaging also plays an important role in diagnosis, staging, response to treatment, and recurrence assessment [5]. Tumor heterogeneity is recognized to be involved in cancer treatment failure, with worse clinical outcomes for highly heterogeneous tumors [6,7]. This leads to the existence of tumor sub-regions with different biological behavior (some more aggressive and treatment-resistant than others) [8-10]. Which are characterized by a different pattern of vascularization, vessel permeability, metabolism, cell proliferation, cell death, and other features, that can be measured by modern medical imaging techniques, including positron emission tomography/computed tomography (PET/CT) [10-12]. Thus, the assessment of tumor heterogeneity through medical images could allow the prediction of therapy response and long-term outcomes of patients with cancer [13]. PET/CT has become essential in oncology [14,15] and is usually evaluated through semiquantitative metabolic parameters, such as maximum/mean standard uptake value (SUVmax, SUVmean) or metabolic tumor volume (MTV), which are valuables as prognostic image-based biomarkers in several tumors [16-17], but these do not assess tumor heterogeneity. Likewise, fluorodeoxyglucose (18F-FDG) PET/CT is important to differentiate malignant from benign solitary pulmonary nodules (SPN), reducing so the number of patients who undergo unnecessary surgical biopsies. Several publications have shown that some quantitative image features, extracted from medical images, are suitable for diagnosis, tumor staging, the prognosis of treatment response, and long-term evolution of cancer patients [18-20]. The process of extracting and relating image features with clinical or biological variables is called “Radiomics” [9,20-24]. Radiomic parameters, such as textural features have been related directly to tumor heterogeneity [25]. This thesis investigated the relationships of the tumor heterogeneity, assessed by 18F-FDG-PET/CT texture analysis, with metabolic parameters and pathologic staging in patients with NSCLC, and explored the diagnostic performance of different metabolic, morphologic, and clinical criteria for classifying (malignant or not) of solitary pulmonary nodules (SPN). Furthermore, 18F-FDG-PET/CT radiomic features of patients with recurrent/metastatic breast cancer were used for constructing predictive models of response to the chemotherapy, based on an optimal combination of several feature selection and machine learning (ML) methods...El cáncer es una de las principales causas de morbilidad y mortalidad. Los más frecuentes son el carcinoma de pulmón de células no pequeñas (NSCLC) y el cáncer de mama, siendo su tratamiento un reto. El diagnóstico se suele realizar mediante biopsia. La heterogeneidad tumoral (HT) está implicada en el fracaso del tratamiento del cáncer, con peores resultados clínicos para tumores muy heterogéneos. Esta conduce a la existencia de subregiones tumorales con diferente comportamiento biológico (algunas más agresivas y resistentes al tratamiento); las cuales se caracterizan por diferentes patrones de vascularización, permeabilidad de los vasos sanguíneos, metabolismo, proliferación y muerte celular, que se pueden medir mediante imágenes médicas, incluida la tomografía por emisión de positrones/tomografía computarizada con fluorodesoxiglucosa (18F-FDG-PET/CT). La evaluación de la HT a través de imágenes médicas, podría mejorar la predicción de la respuesta al tratamiento y de los resultados a largo plazo, en pacientes con cáncer. La 18F-FDG-PET/CT es esencial en oncología, generalmente se evalúa con parámetros metabólicos semicuantitativos, como el valor de captación estándar máximo/medio (SUVmáx, SUVmedio) o el volumen tumoral metabólico (MTV), que tienen un gran valor pronóstico en varios tumores, pero no evalúan la HT. Asimismo, es importante para diferenciar los nódulos pulmonares solitarios (NPS) malignos de los benignos, reduciendo el número de pacientes que van a biopsias quirúrgicas innecesarias. Publicaciones recientes muestran que algunas características cuantitativas, extraídas de las imágenes médicas, son robustas para diagnóstico, estadificación, pronóstico de la respuesta al tratamiento y la evolución, de pacientes con cáncer. El proceso de extraer y relacionar estas características con variables clínicas o biológicas se denomina “Radiomica”. Algunos parámetros radiómicos, como la textura, se han relacionado directamente con la HT. Esta tesis investigó las relaciones entre HT, evaluada mediante análisis de textura (AT) de imágenes 18F-FDG-PET/CT, con parámetros metabólicos y estadificación patológica en pacientes con NSCLC, y exploró el rendimiento diagnóstico de diferentes criterios metabólicos, morfológicos y clínicos para la clasificación de NPS. Además, se usaron características radiómicas de imágenes 18F-FDG-PET/CT de pacientes con cáncer de mama recurrente/metastásico, para construir modelos predictivos de la respuesta a la quimioterapia, combinándose varios métodos de selección de características y aprendizaje automático (ML)...Fac. de Ciencias FísicasTRUEunpu

Assessment and optimisation of 3D optical topography for brain imaging

Optical topography has recently evolved into a widespread research tool for non-invasively mapping blood flow and oxygenation changes in the adult and infant cortex. The work described in this thesis has focused on assessing the potential and limitations of this imaging technique, and developing means of obtaining images which are less artefactual and more quantitatively accurate. Due to the diffusive nature of biological tissue, the image reconstruction is an ill-posed problem, and typically under-determined, due to the limited number of optodes (sources and detectors). The problem must be regularised in order to provide meaningful solutions, and requires a regularisation parameter (\lambda), which has a large influence on the image quality. This work has focused on three-dimensional (3D) linear reconstruction using zero-order Tikhonov regularisation and analysis of different methods to select the regularisation parameter. The methods are summarised and applied to simulated data (deblurring problem) and experimental data obtained with the University College London (UCL) optical topography system. This thesis explores means of optimising the reconstruction algorithm to increase imaging performance by using spatially variant regularisation. The sensitivity and quantitative accuracy of the method is investigated using measurements on tissue-equivalent phantoms. Our optical topography system is based on continuous-wave (CW) measurements, and conventional image reconstruction methods cannot provide unique solutions, i.e., cannot separate tissue absorption and scattering simultaneously. Improved separation between absorption and scattering and between the contributions of different chromophores can be obtained by using multispectral image reconstruction. A method is proposed to select the optimal wavelength for optical topography based on the multispectral method that involves determining which wavelengths have overlapping sensitivities. Finally, we assess and validate the new three-dimensional imaging tools using in vivo measurements of evoked response in the infant brain