Usually, image compression techniques that use only one transform exhibit some poor properties. For instance, the Discrete Cosine Transform (DCT) cannot efficiently represent high frequency components, resulting in blurred images. The Multiple Bases Representation (MBR) compression technique, which uses two or more transforms, is found to be superior to the single transform techniques in terms of representation efficiency. However, some bits in the MBR representation are needed to track the basis information. The MBR image quality is deteriorated by discontinuities at block boundaries, as is the standard DCT transform. In this thesis, test images are distorted by MBR compression using a Recursive Residual Projection algorithm. This algorithm is a sub-optimal method to find the best basis vector subset for representing images based on multiple orthogonal bases. The MBR distorted images are reconstructed by the iterative method of Projection onto Convex Sets (POCS). Many constraints that form convex sets are reviewed and examined. Due to the high distortion at the block boundaries, some constraints are introduced particularly to reduce artifacts at the boundaries. Some constraints add energy to the reconstructed images while others remove energy. Thus, the initial vectors play a key role in the performance of the POCS method for better MBR reconstruction. This thesis also determines the most appropriate initial vector for each constraint. Finally, the composite projections associated with the sign, minimum decreasing and norm-of-slope constraints are used to improve the reconstruction of the MBR distorted images and the effect of ordering of the projections is investigated. / Master of Science

Nesta tese é apresentado um novo método de reconstrução de imagens, por tomografia de transmissão, de projeções sujeitas a ruído na contagem de fótons. O método de reconstrução selecionado utiliza a técnica POCS (Projections Onto Convex Sets). A estimação das projeções originais a partir das observações ruidosas se dá por meio de quatro métodos: a) estimação utilizando o critério MAP (Maximum a Posteriori); b) filtragem nos coeficientes wavelets das projeções ruidosas; c) aplicação do filtro de Wiener pontual e d) aplicação do filtro de Goodman-Belsher. É apresentado o resultado da reconstrução após a estimação das projeções, mostrando o ISNR (Improvement Signal-to-Noise Ratio) entre as imagens reconstruídas, a partir das projeções ruidosas, com a técnica POCS, estimando as projeções e sem a realização da estimação. Foram utilizados, para reconstrução tomográfica, projeções de corpos de prova obtidos por meio de simulação e também projeções obtidas experimentalmente no minitomógrafo do CNPDIA - EMBRAPA. O uso de estimação sobre as projeções ruidosas mostrou-se eficaz para melhorar a relação sinal-ruído na imagem final, pois esse pré-processamento faz com que os conjuntos impostos pelas projeções sejam mais restritivos. Deve-se observar que a melhoria das imagens obtidas com o uso de filtragem das projeções é obtida com uma relação custo-benefício bastante baixa, pois a maior parte do custo computacional está na fase de reconstrução das imagens. / In this thesis is pesented a new method for image reconstruction, by transmission tomography, for projections under noise in the counting of photons. The selected method of reconstruction uses the POCS (Projections Onto Convex Sets) technique. The estimation of the original projections from the noisy projections observed is performed through four methods: a) estimation using the MAP (Maximum a Posteriori) criteria; b) through of filtering of the wavelets coefficients of the noisy projections; c) using the pointwise Wiener filter and d) using the Goodman-Belsher filter. We present the result of reconstruction after projection estimation, showing the ISNR (Improvement Signal-to-Noise Ratio) between the reconstructed images on noisy projections, using POCS technique after the estimated projections and without this estimation. We use, for tomographic reconstruction, test body projections obtained through simulation and also projections obtained experimentally in the minitomograph scanner of CNPDIA-EMBRAPA. The use of estimation on noisy projections demonstrated to be efficient in improving the signalnoise ratio in the final image, since this pre-processing makes the sets that projections more restrictive. We should observe that the use of projection filtering is obtained with a cost-benefit ratio rather low, since the largest part of the computational effort is in the image reconstruction phase.

The body motion of patients, during magnetic resonance (MR) imaging causes significant artifacts in the reconstructed image. Artifacts are manifested as a motion induced blur and ghost repetitions of the moving structures. which obscure vital anatomical and pathological detail. The techniques that have been proposed for suppressing motion artifacts fall into two major categories. Real-time techniques attempt to prevent the motion from corrupting the data by restricting the data acquisition times or motion of the patients, whereas the post-processing techniques use the information embedded in the corrupted data to restore the image. Most methods currently in widespread use belong to the real-time techniques, however with the advent of fast computing platforms and sophisticated signal processing algorithms, the emergence of post-processing techniques is clearly evident. The post-processing techniques usually demand an appropriate model of the motion. The restoration of the image requires that the motion parameters be determined in order to invert the data degradation process. Methods for the correction of translational motion have been studied extensively in the past. The subject of this thesis encompasses the rotational motion model and the effect of rotational motion on the collected MR data in the spatial frequency space (k-space), which is in general, more complicated than the translational model. Rotational motion artifacts are notably prevalent in MR images of head, brain and limbs. Post-processing techniques for the correction of rotational motion artifacts often involve interpolation and re-gridding of the acquired data in the k-space. These methods create significant data overlap and void regions. Therefore, in the past, proposed corrective techniques have been limited to suppression of artifacts caused by small angle rotations. This thesis presents a method of managing overlap regions, using weighted averaging of redundant data, in order to correct for large angle rotations. An iterative estimation technique for filling the data void regions has also been developed by the use of iterated application of projection operators onto constraint sets. These constraint sets are derived from the k-space data generated by the MR imager, and available a priori knowledge. It is shown that the iterative algorithm diverges at times from the required image, due to inconsistency among the constraint sets. It is also shown that this can be overcome by using soft. constraint sets and fuzzy projections. One of the constraints applied in the iterative algorithm is the finite support of the imaged object, marked by the outer boundary of the region of interest (ROI). However, object boundary extraction directly from the motion affected MR image can be difficult, specially if the motion function of the object is unknown. This thesis presents a new ROI extraction scheme based on entropy minimization in the image background. The object rotation function is usually unknown or unable to be measured with sufficient accuracy. The motion estimation algorithm proposed in this thesis is based on maximizing the similarity among the k-space data subjected to angular overlap. This method is different to the typically applied parameter estimation technique based on minimization of pixel energy outside the ROI, and has higher efficiency and ability to estimate rotational motion parameters in the midst of concurrent translational motion. The algorithms for ROI extraction, rotation estimation and data correction have been tested with both phantom images and spin echo MR images producing encouraging results.

The body motion of patients, during magnetic resonance (MR) imaging causes significant artifacts in the reconstructed image. Artifacts are manifested as a motion induced blur and ghost repetitions of the moving structures. which obscure vital anatomical and pathological detail. The techniques that have been proposed for suppressing motion artifacts fall into two major categories. Real-time techniques attempt to prevent the motion from corrupting the data by restricting the data acquisition times or motion of the patients, whereas the post-processing techniques use the information embedded in the corrupted data to restore the image. Most methods currently in widespread use belong to the real-time techniques, however with the advent of fast computing platforms and sophisticated signal processing algorithms, the emergence of post-processing techniques is clearly evident. The post-processing techniques usually demand an appropriate model of the motion. The restoration of the image requires that the motion parameters be determined in order to invert the data degradation process. Methods for the correction of translational motion have been studied extensively in the past. The subject of this thesis encompasses the rotational motion model and the effect of rotational motion on the collected MR data in the spatial frequency space (k-space), which is in general, more complicated than the translational model. Rotational motion artifacts are notably prevalent in MR images of head, brain and limbs. Post-processing techniques for the correction of rotational motion artifacts often involve interpolation and re-gridding of the acquired data in the k-space. These methods create significant data overlap and void regions. Therefore, in the past, proposed corrective techniques have been limited to suppression of artifacts caused by small angle rotations. This thesis presents a method of managing overlap regions, using weighted averaging of redundant data, in order to correct for large angle rotations. An iterative estimation technique for filling the data void regions has also been developed by the use of iterated application of projection operators onto constraint sets. These constraint sets are derived from the k-space data generated by the MR imager, and available a priori knowledge. It is shown that the iterative algorithm diverges at times from the required image, due to inconsistency among the constraint sets. It is also shown that this can be overcome by using soft. constraint sets and fuzzy projections. One of the constraints applied in the iterative algorithm is the finite support of the imaged object, marked by the outer boundary of the region of interest (ROI). However, object boundary extraction directly from the motion affected MR image can be difficult, specially if the motion function of the object is unknown. This thesis presents a new ROI extraction scheme based on entropy minimization in the image background. The object rotation function is usually unknown or unable to be measured with sufficient accuracy. The motion estimation algorithm proposed in this thesis is based on maximizing the similarity among the k-space data subjected to angular overlap. This method is different to the typically applied parameter estimation technique based on minimization of pixel energy outside the ROI, and has higher efficiency and ability to estimate rotational motion parameters in the midst of concurrent translational motion. The algorithms for ROI extraction, rotation estimation and data correction have been tested with both phantom images and spin echo MR images producing encouraging results.

Nesta tese é apresentado um novo método de reconstrução de imagens, por tomografia de transmissão, de projeções sujeitas a ruído na contagem de fótons. O método de reconstrução selecionado utiliza a técnica POCS (Projections Onto Convex Sets). A estimação das projeções originais a partir das observações ruidosas se dá por meio de quatro métodos: a) estimação utilizando o critério MAP (Maximum a Posteriori); b) filtragem nos coeficientes wavelets das projeções ruidosas; c) aplicação do filtro de Wiener pontual e d) aplicação do filtro de Goodman-Belsher. É apresentado o resultado da reconstrução após a estimação das projeções, mostrando o ISNR (Improvement Signal-to-Noise Ratio) entre as imagens reconstruídas, a partir das projeções ruidosas, com a técnica POCS, estimando as projeções e sem a realização da estimação. Foram utilizados, para reconstrução tomográfica, projeções de corpos de prova obtidos por meio de simulação e também projeções obtidas experimentalmente no minitomógrafo do CNPDIA - EMBRAPA. O uso de estimação sobre as projeções ruidosas mostrou-se eficaz para melhorar a relação sinal-ruído na imagem final, pois esse pré-processamento faz com que os conjuntos impostos pelas projeções sejam mais restritivos. Deve-se observar que a melhoria das imagens obtidas com o uso de filtragem das projeções é obtida com uma relação custo-benefício bastante baixa, pois a maior parte do custo computacional está na fase de reconstrução das imagens. / In this thesis is pesented a new method for image reconstruction, by transmission tomography, for projections under noise in the counting of photons. The selected method of reconstruction uses the POCS (Projections Onto Convex Sets) technique. The estimation of the original projections from the noisy projections observed is performed through four methods: a) estimation using the MAP (Maximum a Posteriori) criteria; b) through of filtering of the wavelets coefficients of the noisy projections; c) using the pointwise Wiener filter and d) using the Goodman-Belsher filter. We present the result of reconstruction after projection estimation, showing the ISNR (Improvement Signal-to-Noise Ratio) between the reconstructed images on noisy projections, using POCS technique after the estimated projections and without this estimation. We use, for tomographic reconstruction, test body projections obtained through simulation and also projections obtained experimentally in the minitomograph scanner of CNPDIA-EMBRAPA. The use of estimation on noisy projections demonstrated to be efficient in improving the signalnoise ratio in the final image, since this pre-processing makes the sets that projections more restrictive. We should observe that the use of projection filtering is obtained with a cost-benefit ratio rather low, since the largest part of the computational effort is in the image reconstruction phase.

Made available in DSpace on 2016-06-02T19:06:26Z (GMT). No. of bitstreams: 1 DissMS.pdf: 2267976 bytes, checksum: dfd0f34aeb56928031a68733947fbf11 (MD5) Previous issue date: 2005-09-23 / Computer Optical Sectioning Microscopy (COSM) is widely used in morphological studies of cellular structures. COSM appears as a great challenge to digital image processing, because the large size of the three-dimensional files. The major problem in COSM is the blurring, which practically turn the image unusable without the use of digital image processing techniques. In this work, based on projection onto convex set were developed image processing techniques to restore COSM images, obtained by a confocal microscope. Although confocal microscope presents less blurring than the wide field microscope, it has a larger Poisson noise level. To reduce the Poisson noise the Anscombe Transform (AT) was used as well a pointwise Wiener Filter. The POCS methods were evaluated by means of simulations, using synthetic images (phantom), and the results was evaluated by ISNR (Improvement in Signal Noise Ratio) and UIQ (Universal Quality Index). The developed algorithms, using RAP (Row Action Projection) present satisfactory results, but the computational costs were expensive. / A técnica de Microscopia de Seccionamento Óptico por Computador (COSM) é muito utilizada no estudo morfológico de estruturas celulares. Essa técnica apresenta um grande desafio para a área de processamento de imagens, pois os arquivos tridimensionais possuem grande volume de dados para serem processados. O principal problema do COSM é o borramento existente, que praticamente inviabiliza a utilização dessa imagem sem o uso de técnicas de processamento de imagem. Nesse trabalho, foram desenvolvidas técnicas de projeção em conjuntos convexos POCS (Projection Onto Convex Sets) de processamento de imagens para a restauração das imagens de COSM, obtidas por microscópio confocal. Embora os microscópios confocais apresentem menor borramento da imagem que os microscópios wide field, ele possuem um nível maior de ruído Poisson. Para atenuar o ruído Poisson foi utilizada a Transformada de Anscombe (AT) e o filtro de Wiener pontual. Os métodos POCS, foram avaliados através de simulações utilizando imagens sintéticas (phantoms), e os resultados foram avaliados através do ISNR(Improvement Signal to Noise Ratio) e do UIQ(Universal Quality Index). Os algoritmos desenvolvidos, utilizando RAP (Row Action Projection) apresentaram bons resultados, mas o custo computacional para imagem tridimensional é bastante elevado.

Bildgruppen på enheten för dokument och informationsteknik hos SKL har ett behov av att kunna förbättra bilder med extremt låg upplösning. Detta bildmaterial kan komma från diverse övervakningskameror där det intressanta objektet endast utgör en väldigt liten del, i detta fall registreringsskyltar på förbipasserande bilar. Att skapa en högupplöst bild av en registreringsskylt utav ett fåtal lågupplösta bilder är ett välkänt problem med ett flertal förslag på metoder och lösningar. I denna rapport kommer vi att undersöka vilka metoder som passar bäst vid bildförbättring av registreringsskyltar. Vi kommer även att skapa ett användargränssnitt där man kan läsa in en bild och välja mellan att automatiskt hitta registreringsskylten i bilden eller att manuellt klippa ut den. Efter att man erhållit en bild innehållandes endast registreringsskylten ska de olika implementerade bildförbättringsmetoderna kunna användas. Slutligen diskuteras vilka för- och nackdelar de respektive metoderna har. Förslag på eventuella förbättringar och hur man kan utveckla dessa metoder vidare presenteras därtill.

Avec le besoin croissant en bande-passante, les technologies dites de radio-cognitive sont de plus en plus étudiées par la communauté scientifique. L’enjeu est d’utiliser au mieux le spectre disponible. L'une de ces technologies, Transform Domain Communication System (TDCS), dont les performances en termes d’efficacité énergétique et spectrale étaient jusqu'à présent méconnues, constitue le sujet d'étude de cette thèse. Après une présentation du contexte scientifique et industriel de la thèse, le système TDCS est introduit, ainsi que ses similarités et différences avec OFDM et MC-CDMA. Le système est ensuite décrit sous le formalisme algébrique des modulations linaires. Cela a permis d’établir une expression de l’efficacité spectrale du système. Plusieurs techniques sont alors proposées pour améliorer celle-ci tout en améliorant, dans certains cas, le taux d’erreur binaire. Étant composé d’un de plusieurs composantes sinusoïdales, le signal TDCS souffre d’un fort Peak-to-Average Power Ratio (PAPR). La théorie ensembliste est alors présentée puis mise à profit en troisième partie de cette thèse pour proposer les algorithmes Douglas-Rachford et ROCS de réduction du PAPR des signaux TDCS. Ces algorithmes convergent plus rapidement et vers des valeurs plus basses que l’algorithme POCS précédemment utilisé dans la littérature / For about ten years, spectrum scarcity and the growing need of bandwidth have pushed the studies on cognitive-radio technologies to counter this waste. Among them: the Transform Domain Communication System (TDCS), on which this thesis focuses. Until now, TDCS’ performance in terms of spectral and power efficiency was largely unknown. After introducing the thesis’ industrial and scientific context, the TDCS is introduced and compared with popular technologies such as OFDM and MC-CDMA. The system is then studied by means of the linear modulations’ algebraic framework. This has led to the TDCS’ spectral efficiency determination and to new design rules to jointly achieve a better spectral efficiency and a lower BER. Several methods are then proposed to further increase the spectral efficiency by means of a dense multidimensional modulation. Since a TDCS signal is made of several sines, it suffers from a strong Peak-to-Average Power Ratio (PAPR). Set theoretic estimation is then introduced in a third part and new PAPR-reduction algorithms such as Douglas-Rachford and Reflection Onto Convex Sets are brought to light and achieve better performance than the usual POCS algorithm regarding to the convergence rate, as well as the achieved PAPR

Made available in DSpace on 2016-06-02T19:05:33Z (GMT). No. of bitstreams: 1 DissFVS.pdf: 1180703 bytes, checksum: 9100eb794f6c0baf44418e34c9b1ed49 (MD5) Previous issue date: 2001-08-31 / Financiadora de Estudos e Projetos / In this dissertation four algorithms are presented for the tomographic reconstruction of images using methods denominated POCS - Projections onto Convex Sets, which are the ART - Algebraic Reconstruction Technique, the SIRT - Simultaneous Iterative Reconstructive Technique, the sequencial POCS and parallel POCS. A comparison is made between the reconstruction methods named above, in the presence of noise and in the reconstruction from limited view. In each reconstruction, the result of each iteration is compared with the desired image, also showing the convergence curve for each method. For the tomographic reconstructions, projections from test bodies obtained throught simulation were used and also experimental projections obtained by the mini-tomograph scanner of CNPDIA-EMBRAPA. Although were considered only the reconstruction based an projections obtained with parallel beams, the methods here described can also reconstruct images that are independent of the source-detector geometry used by the tomograph scanner. The use of restrictions over the solutions, as in the case of serial and parallel POCS, demonstrated efficiency in reducing the variability due to the ill-conditioning of the problem. / Nesta dissertação são apresentados quatro algoritmos para reconstrução tomográfica de imagens utilizando o método de projeções em conjuntos convexos (POCS - Projections onto Convex Sets), sendo eles o ART (Algebraic Reconstruction Technique), o SIRT (Simultaneous Iterative Reconstructive Technique), o POCS sequencial e o POCS paralelo. É feita a comparação entre os métodos de reconstrução, acima citados, na presença de ruído e na reconstrução à partir de ângulos limitados. Em cada reconstrução o resultado obtido em cada iteração é comparado com a imagem desejada, mostrando-se também o gráfico de convergência de cada método. Utilizaram-se, para reconstrução tomográfica, projeções de corpos de testes obtidas através de simulação e também projeções obtidas experimentalmente no minitomógrafo do CNPDIA-EMBRAPA. Embora seja considerada somente a reconstrução a partir de projeções obtidas em tomógrafos com feixe de raios paralelos, os métodos expostos podem reconstruir imagens independentemente da geometria fonte-detetor utilizada pelo tomógrafo. O uso de restrições sobre as soluções, como no caso dos métodos POCS sequencial e paralelo, mostrou-se eficaz para reduzir as variações devido ao malcondicionamento do problema.

Made available in DSpace on 2016-06-02T19:06:24Z (GMT). No. of bitstreams: 1 DissJPP.pdf: 1642944 bytes, checksum: 29bcc8056798933f7955167a88e8e000 (MD5) Previous issue date: 2005-02-18 / Financiadora de Estudos e Projetos / The number of applications in remote sensing has widely increased in the last years. The reason for this is mainly the high quality of imaging systems onboard. Among this new generation of satellites, the CBERS-1 (China-Brazil Earth Resources Satellite) was developed through a partnership between Brazil and China, and its main mission is to capture high-resolution images of the Earth using panchromatic and multispectral detectors. However, the information provided by remote sensing needs to be processed to better reflect the radiometric quality of the data, using for this purpose a technique called image restoration. The main goal of image restoration is the reconstruction or recovery of the degraded image using some a priori knowledge of the degradation phenomenon. In this work we developed five image restoration algorithms based on the theory of convex projections, which were obtained through the CBERS-1 band 2 CCD sensor. These algorithms are based on the application of restrictions in convex sets form, through the POCS (Projections Onto Convex Sets) method, where the intersection among these sets, if it exists, gives a satisfactory solution for the problem. The simulations were developed using the RAP (Row-Action Projections), the SIRT (Simultaneous Iterative Reconstruction Technique) and an algorithm that uses prototype image constraints, which were obtained by the methods cited above and by the MIF (Modified Inverse Filter). The results were visually and numerically evaluated. / A quantidade de aplicações oriundas do sensoriamento remoto tem aumentado significativamente nos últimos anos. Isso se deve, principalmente, à alta qualidade dos equipamentos a bordo dos sistemas sensores. Entre essa nova geração de satélites, o CBERS-1 (China-Brazil Earth Resources Satellite) foi desenvolvido através de uma parceria entre Brasil e China, sendo sua missão principal a de capturar imagens de alta resolução da Terra utilizando detectores pancromáticos e multiespectrais. Contudo, as informações oriundas do sensoriamento remoto necessitam ser processadas para melhorar a qualidade radiométrica dos dados, utilizando para tal uma técnica conhecida por restauração de imagens, sendo seu principal objetivo a reconstrução ou recuperação de uma imagem degradada utilizando algum conhecimento a priori do fenômeno de degradação. No presente trabalho foram desenvolvidos cinco algoritmos de restauração de imagens baseados na teoria de projeções convexas, as quais foram obtidas através do sensor CCD da banda 2 do satélite CBERS-1. Estes algoritmos são baseados na aplicação de restrições na forma de conjuntos convexos, através do método de POCS (Projections Onto Convex Sets), sendo que a intersecção entre esses conjuntos, caso exista, fornece uma solução satisfatória para o problema. As simulações foram desenvolvidas utilizando o RAP (Row-Action Projections), SIRT (Simultaneous Iterative Reconstruction Technique) e um algoritmo que utiliza uma restrição de imagem protótipo, a qual foi obtida pelos métodos citados acima e pelo FIM (Filtro Inverso Modificado). Os resultados foram avaliados visualmente e através de análises numéricas.