Reconstrução de imagens de tomografia por emissão de pósitrons com base em compressive sensing e informação a priori

Dissertação (Mestrado em Engenharia Biomédica) — Universidade de Brasília, Faculdade UnB Gama, Programa de pós-graduação em Engenharia Biomédica, 2021.A Tomografia por Emissão de Pósitrons(PET), é um exame diagnóstico no âmbito do imageamento médico não invasivo. Ela utiliza, em pequenas quantidades, materiais radioativos denominados radiofármacos, para o diagnóstico de doenças por meio de imagens. Essa técnica combina informações anatômicas e metabólicas, que permitem a detecção de doenças em fases iniciais ao medir a atividade em nível celular no corpo humano. É amplamente usada no tratamento de doenças gastrointestinais, endócrinas, cardíacas e de diversos tipos de câncer. Contudo, o custo de exame PET e o tempo de aquisição dos dados limitam seu uso. Algoritmos de reconstrução alternativos aos tradicionais têm sido desenvolvidos com o propósito de diminuir a quantidade de medidas necessárias ou o tempo em que essas medidas são adquiridas pelo escâner de PET. Uma forma de buscar esse objetivo é utilizar técnicas de reconstrução de dados sub-amostrados baseadas em Compressive Sensing(CS).O CSpermite reconstruir as imagens a partir de uma quantidade de medidas inferior à definida pelo critério de Nyquist. Nessas condições, é fundamental que exista um domínio transformado conhecido em que o sinal seja esparso e que as medidas sejam em números suficientes, o que depende do grau de esparsidade. Além disso, é necessário que o domínio em que o sinal é esparso seja incoerente com relação ao domínio de medidas.Outra abordagem que também permite uma melhora da relação entre qualidade de imagem e o número de medidas é a Pré-filtragem, uma técnica que combinada com CSpermite reduzir o número de coeficientes necessários para a reconstrução. O princípio se baseia na geração de imagens pré-filtradas em uma primeira etapa, de forma a favorecer a esparsidade em cada versão reconstruída. Posteriormente, uma etapa de composição espectral gera a imagem objetivo a partir das versões filtradas. Além disso, a informação de suporte constitui outro método que usado junto aos anteriores também diminui o tempo de aquisição dos dados, com base nas informações de cortes ou quadros prévios. De fato, o uso de Pré-filtragem e o uso de Informação a priori têm melhorado a qualidade de reconstrução de imagens em algumas técnicas de imageamento, sobretudo na Ressonância Magnética. No entanto, não foram encontrados esses algoritmos como referência na literatura para imagens de PET, provavelmente pelas dificuldades adicionais de aplicar um processo de medição computacional e seu operador adjunto que é necessário para implementação de CS.Diante desses desafios, nesse trabalho foram implementados os algoritmos de CScom Pré-filtragem, para reconstrução de sinais com uso de informação a priori, para o caso de medidas de PET. Os algoritmos, uma vez implementados, foram utilizados também sem informação a priori, para efeito de comparação. A implementação exigiu programas de otimização (minimização de l1e de lp), realizados em Octave. Para avaliação desses algoritmos, foram utilizadas imagens de um banco de dados de Tomografia por Emissão de Pósitronsnomeado Laboratóriode Neuroimagem(LONI) Image and DATA Archive(IDA).Os valoresdas medidas de PET foram calculados a partir das imagens obtidas do banco de dados e então reconstruídas empregando os algoritmos clássicos para PET (retroprojeção filtrada), CScom Pré-filtragem sem informação a priori e, por fim, o CScom Pré-filtragem. Foi feita uma comparação da relação sinal erro das imagens reconstruídas a partir de cada método. Também foi realizada uma série de análises da qualidade de reconstrução de imagens à medida em que se aumenta o número de linhas radiais. Os resultados sugerem que as imagens reconstruídas pelo método propostos são associadas a uma melhor qualidade em termos de relação sinal erro (p=3.9874e-63) em comparação com a retroprojeção filtrada. Os testes estatísticos realizados sugerem que as imagens reconstruídas pelo método proposto (CScom Pré-filtragem e informações a priori) resultam em uma melhor qualidade média da imagem em comparação aos outros dois métodos. Foram realizados testes preliminares com informação a priori com sinais de domínio unidimensional que mostraram que esses resultados melhoram em termos de SNR (dB) a qualidade da imagem reconstruída. Além disso, foi investigado o impacto que essa informação a priori pode ter nas imagens PET. Foram consideradas sequências de imagens que representam diferentes quadros temporais (ouframes). A informação que pode ser extraída de um quadro é utilizada para auxiliar na reconstrução do próximo quadro. Ao final, foi avaliado o impacto que isso tem em termos da qualidade da reconstrução conforme medida pela SNR (dB), apresentando os melhores resultados em imagens de dimensões maiores.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).Positron emission tomography (PET) is a diagnostic method within non-invasive medical imaging, which uses small amounts of radioactivematerials called radiopharmaceuticals for the diagnosis of diseases using images. This technique combines anatomical and metabolic information and allows the detection of diseases early when measuring activity at the cellular level in the human body. Different types of treatment procedures for gastrointestinal, endocrine, and heart conditions, as well as for various types of cancer, use this technique.However, the cost of PET examination and the time of data acquisition limit its use.Alternative reconstruction algorithms to the traditional ones have been developed to reduce the number of necessary measurements or the time in which the PET scanner acquires these measures. One way to achieve this goal is to use sub-sampled data reconstruction techniques based on Compressive Sensing (CS). This technique makes it possible to reconstruct the images starting with a smaller number of measurements, as compared to that defined by the Nyquist criterion. In these conditions, it is necessary to satisfy the requirement that there is a transformed domain where the signal is sparse.Prefiltering is a technique that, combined with compressive sensing, reduces the number of coefficients required for reconstruction, by first generating filtered versions of the desired image. The used filters are chosen in order to favor image sparsity, thus improving reconstruction by CS. Also, the use of support prior information constitutes another method that can be used in combination with CS and pre-filtering, and which also decreases the time used for data acquisition by exploring aspects of previous time frames or image slices.The use of pre-filtering, as well as the use of prior-information, has improved the quality of image reconstruction in some imaging techniques, especially Magnetic Resonance. However, these algorithms were not found as a reference in the literature for PET images, probably due to the additional difficulties of applying a computational measurement process and its assistant operator that is necessary for implementing CS.In this work, we implemented and evaluated our proposed method for reconstructing PET images using prior information. The algorithms were also used without prior information, for comparison purposes. The implementation required optimization programs (l1and lpminimization), which we implemented in Octave.We used images from a PET database named LONI Image and Data Archive (IDA) in order to evaluate these algorithms.In our experiments, we computed the values of the PET measurements starting from sample images obtained from the database. Then we reconstructed each image(using the measurements only, as in the real context) using the classic algorithms for PET (filtered back projection), compressive sensing with prefiltering without prior information, and finally compressive sensing with prefiltering and prior information. We made a comparison of the signal-to-noise ratios of the reconstructed images using each method. Also, we performed an analysis of the quality of image reconstruction as the number of radial lines increases. The results suggest that the proposed method significantly improves the reconstruction process in terms of objective image quality, in comparison with the filtered back projection approach.The statistical tests we used suggest that, with statistical significance, the images reconstructed by the proposed method (CS with prefiltering and a priori information) results in better average image quality compared to the other two methods.Furthermore, the impact that this a priori information may have on PET images was investigated. We considered sequences of images that represent different frames. Information that can be extracted from one frame was used to aid in the reconstruction of the following frame. At the end, the impact this has in terms of the quality of the reconstruction as measured by the SNR(dB) was evaluated, showing reconstruction improvements specially for larger images

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