Parâmetro de regularização em problemas inversos: estudo numérico com a transformada de Radon

In general, an inverse problem corresponds to find a value of an element x in a suitable vector space, given a vector y measuring it, in some sense. When we discretize the problem, it usually boils down to solve an equation system f(x) = y, where f : U Rm ! Rn represents the step function in any domain U of the appropriate Rm. As a general rule, we arrive to an ill-posed problem. The resolution of inverse problems has been widely researched along the last decades, because many problems in science and industry consist in determining unknowns that we try to know, by observing its effects under certain indirect measures. Our general subject of this dissertation is the choice of Tykhonov´s regulaziration parameter of a poorly conditioned linear problem, as we are going to discuss on chapter 1 of this dissertation, focusing on the three most popular methods in nowadays literature of the area. Our more specific focus in this dissertation consists in the simulations reported on chapter 2, aiming to compare the performance of the three methods in the recuperation of images measured with the Radon transform, perturbed by the addition of gaussian i.i.d. noise. We choosed a difference operator as regularizer of the problem. The contribution we try to make, in this dissertation, mainly consists on the discussion of numerical simulations we execute, as is exposed in Chapter 2. We understand that the meaning of this dissertation lays much more on the questions which it raises than on saying something definitive about the subject. Partly, for beeing based on numerical experiments with no new mathematical results associated to it, partly for being about numerical experiments made with a single operator. On the other hand, we got some observations which seemed to us interesting on the simulations performed, considered the literature of the area. In special, we highlight observations we resume, at the conclusion of this work, about the different vocations of methods like GCV and L-curve and, also, about the optimal parameters tendency observed in the L-curve method of grouping themselves in a small gap, strongly correlated with the behavior of the generalized singular value decomposition curve of the involved operators, under reasonably broad regularity conditions in the images to be recovered

Análise da toxicidade no açude Riacho da Cachoeira, Lajes Pintadas (RN): um desafio interdisciplinar

Contamination by complex mixtures of various origins has been explored and studied for decades. Radon is a naturally occurring environmental contaminant that causes carcinogenic effects. These emissions can cause mutations in the lung tissue, which can initiate a carcinogenic process. Thus the dam Creek Falls, located in the municipality of Lajes Pintadas, was chosen for the development of this study, since cancer rates in the region reach 9% of the population annually, with this, the main objective of this study was evaluate the mutagenicity and toxicity of Riacho da Cachoeira damunder the influence of radon. The methodology ecotoxicological tests were performed with Ceriodaphinia dubia, as well as tests with Tradescantia pallida genotoxicologicos and Oreochromis niloticus. To understand how the population of Pintadas Slabs realizes the environment, we performed a study of environmental perception. The test results indicated that the reservoir water is toxic to test organimos exposed, found heavy metals, chloride, total and fecal coliforms as well as radon levels above the maximum allowed under Brazilian law. These results can be justified because it is so complex samples composed of different compounds that interact only with each other or causing synergistic effects. It was concluded that the dam Creek Waterfall, is contaminated with radon, as well as heavy metals, coliforms and chloride, causing toxic effects to the natural community. Thus, further studies should be performed with the human population of the region, to verify that the high rates of cancer in the population of the municipality may be linked to the presence of natural radiation. Thus, it is expected that the competent bodies that administer the municipality of Lajes Pintadas take reasonable steps to minimize risks and ensure the health of the community that still makes use of the weir

Avaliação do potencial mutagênico da água do açude de Lucrécia (RN- Brasil): um enfoque na relação saúde e ambiente

The water quality of many reservoirs in the world has been reduced due to percolation of contaminants to water, which can have natural or anthropogenic origin, increasing the level of genotoxic compounds in aquatic ecosystems. This fact has contributed to the reduction of environmental quality, and commitment the health of living beings that inhabit these ecosystems, including the human population. In this backdrop of reduced water quality, is the Lucrecia dam, which is a major surface water reservoirs by volume of semi-arid region of Rio Grande do Norte, and that has shown contamination by heavy metals, cyanobacteria toxic and the natural presence of Radon. The population that use this source has been showing high rates of cancer, popularly associated with the consumption of this water, with a prevalence about three times higher compared to the whole state of Rio Grande do Norte. Based on this, the present study aimed to evaluate the mutagenic potencial of surface water from the Lucrecia dam, using the Micronucleus Test in Tradescantia pallida (Trad-MN) and in human peripheral blood lymphocytes (CBMN) assay, as well as identify the concentrations of some heavy metals in this water. Water samples were collected on a dry season and a rainy season, in two distinct points. Moreover, in order to bring a completely view about the relationship of man-health-environment in this local, through the knowledge of knowing / acting environmental from residents of Lucrecia, and the use and perceptions they have about the dam of your city, a study of Environmental Perception was carried out with local residents. The results obtained for the both micronucleus test, showed significant results for the three points analyzed. The strongest mutagenic effect was observed in the dry season for both assays. Chemical analyses detected an increase of heavy metal levels in different points and season above the maximum allowed by legislation. Regarding the study of Environmental Perception with local residents, it was observed the knowledge of the environment that the residents have, as well as the strong ties and perceptions with the dam of the city. Thus, the combination of these two aspects (the genetic toxicity tests conducted in the dam together with analysis of environmental perception with the residents of Lucrecia) allowed to draw a more complete diagnosis on the local situation

Recuperação de sinais esparsos. Investigação numérica sobre a quantidade de medidas necessárias para recuperar um sinal esparso

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Influência da radiação ionizante natural no açude do boqueirão (RN): avaliação de risco saúde/ambiente

The contamination of water bodies with toxic substances causes a decrease in water quality, representing a risk to public health. In this context, human activities are generally seen as the main sources of water degradation. However, elements found naturally in the environment can also compromise water quality. Thus, the Boqueirão‘s dam, located in the municipality of Parelhas (RN, Brazil), was chosen as area for the development of this study, as its geological region is rich in the emission of natural ionizing radiation that produces byproducts like lead and Radon. Moreover, the area has a strong human influence that enhances the risks of pollutant discharge in this body of water.Thus, the objectives of this study were centered (i) in the analysis of risk perception in the city of Parelhas (RN/Brasil) due to the use of the water from the Boqueirão Dam; and (ii) in the assessment of water quality in the Dam using methods that quantify, mainly, heavy metals and radiation levels, as well as these toxics potential of inducing mutations on genetic material. The analysis of risk perception showed that the population in the city of Parelhas can perceive a risk in using the water from the dam and that they can recognize factors that influence the water quality. Regarding the second objective, the set of data point to the contamination of the Dam by heavy metals, as well as levels of radioactive parcicles and Radon – also present in high concentrations in outdoor air and on soil. Thus, it is possible to infer that the population residing in this area is subjected to injuries caused by exposure to natural and anthropogenic contamination. Our findings corroborate with the perception of the population regarding the risks associated with the use of the Dam for several types of activities. It is expected that the information gathered in this study can substantiate activities and future researches in this semiarid region in the Rio Grande do Norte/Brazil. Also, that the set of data can enable a better understanding of the specific toxicological scenario of risk found for the population and the effect of the contamination for the biota, which aids the development of a future risk assessment and a consequent management of this local issue.

Resolução em tomografia de tempo de trânsito poço-a-poço: a dependência da iluminação

The key aspect limiting resolution in crosswell traveltime tomography is illumination, a well known result but not as well exemplified. Resolution in the 2D case is revisited using a simple geometric approach based on the angular aperture distribution and the Radon Transform properties. Analitically it is shown that if an interface has dips contained in the angular aperture limits in all points, it is correctly imaged in the tomogram. By inversion of synthetic data this result is confirmed and it is also evidenced that isolated artifacts might be present when the dip is near the illumination limit. In the inverse sense, however, if an interface is interpretable from a tomogram, even an aproximately horizontal interface, there is no guarantee that it corresponds to a true interface. Similarly, if a body is present in the interwell region it is diffusely imaged in the tomogram, but its interfaces - particularly vertical edges - can not be resolved and additional artifacts might be present. Again, in the inverse sense, there is no guarantee that an isolated anomaly corresponds to a true anomalous body because this anomaly can also be an artifact. Jointly, these results state the dilemma of ill-posed inverse problems: absence of guarantee of correspondence to the true distribution. The limitations due to illumination may not be solved by the use of mathematical constraints. It is shown that crosswell tomograms derived by the use of sparsity constraints, using both Discrete Cosine Transform and Daubechies bases, basically reproduces the same features seen in tomograms obtained with the classic smoothness constraint. Interpretation must be done always taking in consideration the a priori information and the particular limitations due to illumination. An example of interpreting a real data survey in this context is also presented.

Resolução em tomografia de tempo de trânsito poço-a-poço: a dependência da iluminação

The key aspect limiting resolution in crosswell traveltime tomography is illumination, a well known result but not as well exemplified. Resolution in the 2D case is revisited using a simple geometric approach based on the angular aperture distribution and the Radon Transform properties. Analitically it is shown that if an interface has dips contained in the angular aperture limits in all points, it is correctly imaged in the tomogram. By inversion of synthetic data this result is confirmed and it is also evidenced that isolated artifacts might be present when the dip is near the illumination limit. In the inverse sense, however, if an interface is interpretable from a tomogram, even an aproximately horizontal interface, there is no guarantee that it corresponds to a true interface. Similarly, if a body is present in the interwell region it is diffusely imaged in the tomogram, but its interfaces - particularly vertical edges - can not be resolved and additional artifacts might be present. Again, in the inverse sense, there is no guarantee that an isolated anomaly corresponds to a true anomalous body because this anomaly can also be an artifact. Jointly, these results state the dilemma of ill-posed inverse problems: absence of guarantee of correspondence to the true distribution. The limitations due to illumination may not be solved by the use of mathematical constraints. It is shown that crosswell tomograms derived by the use of sparsity constraints, using both Discrete Cosine Transform and Daubechies bases, basically reproduces the same features seen in tomograms obtained with the classic smoothness constraint. Interpretation must be done always taking in consideration the a priori information and the particular limitations due to illumination. An example of interpreting a real data survey in this context is also presented.