Computer-aided detection and diagnosis of breast cancer in 2D and 3D medical imaging through multifractal analysis

This Thesis describes the research work performed in the scope of a doctoral research program and presents its conclusions and contributions. The research activities were carried on in the industry with Siemens S.A. Healthcare Sector, in integration with a research team. Siemens S.A. Healthcare Sector is one of the world biggest suppliers of products, services and complete solutions in the medical sector. The company offers a wide selection of diagnostic and therapeutic equipment and information systems. Siemens products for medical imaging and in vivo diagnostics include: ultrasound, computer tomography, mammography, digital breast tomosynthesis, magnetic resonance, equipment to angiography and coronary angiography, nuclear imaging, and many others. Siemens has a vast experience in Healthcare and at the beginning of this project it was strategically interested in solutions to improve the detection of Breast Cancer, to increase its competitiveness in the sector. The company owns several patents related with self-similarity analysis, which formed the background of this Thesis. Furthermore, Siemens intended to explore commercially the computer- aided automatic detection and diagnosis eld for portfolio integration. Therefore, with the high knowledge acquired by University of Beira Interior in this area together with this Thesis, will allow Siemens to apply the most recent scienti c progress in the detection of the breast cancer, and it is foreseeable that together we can develop a new technology with high potential. The project resulted in the submission of two invention disclosures for evaluation in Siemens A.G., two articles published in peer-reviewed journals indexed in ISI Science Citation Index, two other articles submitted in peer-reviewed journals, and several international conference papers. This work on computer-aided-diagnosis in breast led to innovative software and novel processes of research and development, for which the project received the Siemens Innovation Award in 2012. It was very rewarding to carry on such technological and innovative project in a socially sensitive area as Breast Cancer.No cancro da mama a deteção precoce e o diagnóstico correto são de extrema importância na prescrição terapêutica e caz e e ciente, que potencie o aumento da taxa de sobrevivência à doença. A teoria multifractal foi inicialmente introduzida no contexto da análise de sinal e a sua utilidade foi demonstrada na descrição de comportamentos siológicos de bio-sinais e até na deteção e predição de patologias. Nesta Tese, três métodos multifractais foram estendidos para imagens bi-dimensionais (2D) e comparados na deteção de microcalci cações em mamogramas. Um destes métodos foi também adaptado para a classi cação de massas da mama, em cortes transversais 2D obtidos por ressonância magnética (RM) de mama, em grupos de massas provavelmente benignas e com suspeição de malignidade. Um novo método de análise multifractal usando a lacunaridade tri-dimensional (3D) foi proposto para classi cação de massas da mama em imagens volumétricas 3D de RM de mama. A análise multifractal revelou diferenças na complexidade subjacente às localizações das microcalci cações em relação aos tecidos normais, permitindo uma boa exatidão da sua deteção em mamogramas. Adicionalmente, foram extraídas por análise multifractal características dos tecidos que permitiram identi car os casos tipicamente recomendados para biópsia em imagens 2D de RM de mama. A análise multifractal 3D foi e caz na classi cação de lesões mamárias benignas e malignas em imagens 3D de RM de mama. Este método foi mais exato para esta classi cação do que o método 2D ou o método padrão de análise de contraste cinético tumoral. Em conclusão, a análise multifractal fornece informação útil para deteção auxiliada por computador em mamogra a e diagnóstico auxiliado por computador em imagens 2D e 3D de RM de mama, tendo o potencial de complementar a interpretação dos radiologistas

Bayesian Estimation of the Multifractality Parameter for Image Texture Using a Whittle Approximation

International audienceTexture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the 2D dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold. The construction of a generic semiparametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64 × 64 pixels

Multifractal analysis for multivariate data with application to remote sensing

Texture characterization is a central element in many image processing applications. Texture analysis can be embedded in the mathematical framework of multifractal analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, the coefficients or wavelet leaders. Although successfully applied in various contexts, multi fractal analysis suffers at present from two major limitations. First, the accurate estimation of multifractal parameters for image texture remains a challenge, notably for small sample sizes. Second, multifractal analysis has so far been limited to the analysis of a single image, while the data available in applications are increasingly multivariate. The main goal of this thesis is to develop practical contributions to overcome these limitations. The first limitation is tackled by introducing a generic statistical model for the logarithm of wavelet leaders, parametrized by multifractal parameters of interest. This statistical model enables us to counterbalance the variability induced by small sample sizes and to embed the estimation in a Bayesian framework. This yields robust and accurate estimation procedures, effective both for small and large images. The multifractal analysis of multivariate images is then addressed by generalizing this Bayesian framework to hierarchical models able to account for the assumption that multifractal properties evolve smoothly in the dataset. This is achieved via the design of suitable priors relating the dynamical properties of the multifractal parameters of the different components composing the dataset. Different priors are investigated and compared in this thesis by means of numerical simulations conducted on synthetic multivariate multifractal images. This work is further completed by the investigation of the potential benefit of multifractal analysis and the proposed Bayesian methodology for remote sensing via the example of hyperspectral imaging

Bayesian estimation of the parameters of the joint multifractal spectrum of signals and images

Multifractal analysis has become a reference tool for signal and image processing. Grounded in the quantification of local regularity fluctuations, it has proven useful in an increasing range of applications, yet so far involving only univariate data (scalar-valued time series or single channel images). Recently the theoretical ground for multivariate multifractal analysis has been devised, showing potential for quantifying transient higher-order dependence beyond linear correlation among collections of data. However, the accurate estimation of the parameters associated with a multivariate multifractal model remains challenging, severely limiting their actual use in applications. The main goal of this thesis is to propose and study practical contributions on multivariate multifractal analysis of signals and images. Specifically, the proposed approach relies on a novel and original joint Gaussian model for the logarithm of wavelet leaders and leverages on a Whittle-based likelihood approximation and data augmentation for the matrix-valued parameters of interest. This careful design enables efficient estimation procedures to be constructed for two relevant choices of priors using Bayesian inference. Algorithms based on Monte Carlo Markov Chain and Expectation Maximization strategies are designed and used to approximate the Bayesian estimators. Monte Carlo simulations, conducted on synthetic multivariate signals and images with various sample sizes, numbers of components and multifractal parameter settings, demonstrate significant performance improvements over the state of the art. In addition, theoretical lower bounds on the variance of the estimators are designed to study their asymptotic behavior. Finally, the relevance of the proposed multivariate multifractal estimation framework is shown for two real-world data examples: drowsiness detection from multichannel physiological signals and potential remote sensing applications in multispectral satellite imagery

Análisis, procesamiento y modelización de señales y sistemas biomédicos

Las señales biomédicas, tales como el electrocardiograma, electroencefalograma o la señal de voz, tienen en común características de no estacionariedad y no linealidad. En muchas aplicaciones, sin embargo, se supone que se trata de señales estacionarias procedentes de sistemas lineales. Esta simplificación puede considerarse como una hipótesis de trabajo válida sólo como una aproximación que permite la aplicación de las técnicas clásicas de procesamiento de señales. No obstante, es conocido que los trastornos que afectan a uno o más órganos pueden detectarse mediante un correcto análisis de las señales en cuya producción están involucrados. Es aquí donde debe prestarse especial atención a que las señales provenientes de sistemas con alguna patología se alejan aún más de las condiciones hipotéticas de estacionariedad y linealidad. Por esta razón resulta necesario el abordaje de las señales biomédicas mediante herramientas de análisis de señales en un marco que considere las condiciones de no estacionariedad y no linealidad. Basándonos en los antecedentes del grupo de trabajo en técnicas tales como teoría de la información, transformada ondita, descomposición empírica en modos, análisis multifractal, reconocimiento de patrones e inteligencia computacional, se propone el desarrollo de nuevas técnicas que ayuden al abordaje de este problema

Use of wavelet-packet transforms to develop an engineering model for multifractal characterization of mutation dynamics in pathological and nonpathological gene sequences

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the Chaos Game Representation (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, a recently developed technique from the field of signal processing. A multi-fractal model is built by using wavelet transforms to estimate the Hurst exponent, H. The Hurst exponent is a non-parametric measurement of the dynamism of a system. This procedure is used to evaluate gene-coding events in the DNA sequence of cystic fibrosis mutations. The H exponent is calculated for various mutation sites in this gene. The results of this study indicate the presence of anti-persistent, random walks and persistent sub-periods in the sequence. This indicates the hypothesis of a multi-fractal model of DNA information encoding warrants further consideration.;This work examines the model\u27s behavior in both pathological (mutations) and non-pathological (healthy) base pair sequences of the cystic fibrosis gene. These mutations both natural and synthetic were introduced by computer manipulation of the original base pair text files. The results show that disease severity and system information dynamics correlate. These results have implications for genetic engineering as well as in mathematical biology. They suggest that there is scope for more multi-fractal models to be developed