User/relay selection is a simple technique that achieves spatial diversity in multiuser networks. However, for user/relay selection algorithms to make a selection decision, channel state information (CSI) from all cooperating users/relays is usually required at a central node. This requirement poses two important challenges. Firstly, CSI acquisition generates a great deal of feedback overhead (air-time) that could result in significant transmission delays. Secondly, the fed-back channel information is usually corrupted by additive noise. This could lead to transmission outages if the central node selects the set of cooperating relays based on inaccurate feedback information. Motivated by the aforementioned challenges, we propose a limited feedback user/relay selection scheme that is based on the theory of compressed sensing. Firstly, we introduce a limited feedback relay selection algorithm for a multicast relay network. The proposed algorithm exploits the theory of compressive sensing to first obtain the identity of the “strong” relays with limited feedback air-time. Following that, the CSI of the selected relays is estimated using minimum mean square error estimation without any additional feedback. To minimize the effect of noise on the fed-back CSI, we introduce a back-off strategy that optimally backs-off on the noisy received CSI. In the second part of the thesis, we propose a feedback reduction scheme for full-duplex relay-aided multiuser networks. The proposed scheme permits the base station (BS) to obtain channel state information (CSI) from a subset of strong users under substantially reduced feedback overhead. More specifically, we cast the problem of user identification and CSI estimation as a block sparse signal recovery problem in compressive sensing (CS). Using existing CS block recovery algorithms, we first obtain the identity of the strong users and then estimate their CSI using the best linear unbiased estimator (BLUE). Moreover, we derive the error covariance matrix of the post-detection noise to be used in the back-off strategy. In addition to this, we provide exact closed form expressions for the average maximum equivalent SNR at the destination user. The last part of the thesis treats the problem of user selection in a network MIMO setting. We propose a distributed user selection strategy that is based on a well known technique called semi-orthogonal user selection when the zero-forcing beamforming (ZFBF) is adopted. Usually this technique requires perfect channel state information at the transmitter (CSIT) which might not be available or need large feedback overhead. Instead, we propose a distributed user selection technique where no communication between base stations is needed. In order to reduce the feedback overhead, each user set a timer that is inversely proportional to his channel quality indicator (CQI). This technique will allow only the user with the highest CQI to feedback provided that the transmission time is shorter than the difference between his timer and the second strongest user timer, otherwise a collision will occur. In the case of collision, we propose another feedback strategy that is based on the theory of compressive sensing, where collision is allowed and each user encode its feedback using Gaussian codewords and feedback the combination at the same time with other users. We prove that the problem can be formulated as a block sparse recovery problem and that this approach is agnostic on the transmission time, thus it could be a good alternative to the timer approach when collision is dominant. Simulation results show that the proposed CS-based selection algorithms yield a rate performance that is close to the ones achieved when perfect CSI is available while consuming a small amount of feedback.

No description available.

Recent research has shown that compressible signals can be recovered from a very limited number of measurements by minimizing nonconvex functions that closely resemble the L0-norm function. These functions have sparse minimizers and, therefore, are called sparsity-promoting functions (SPFs). Recovery is achieved by solving a nonconvex optimization problem when using these SPFs. Contemporary methods for the solution of such difficult problems are inefficient and not supported by robust convergence theorems. New signal-recovery methods for compressive sensing that can be used to solve nonconvex problems efficiently are proposed. Two categories of methods are considered, namely, sequential convex formulation (SCF) and proximal-point (PP) based methods. In SCF methods, quadratic or piecewise-linear approximations of the SPF are employed. Recovery is achieved by solving a sequence of convex optimization problems efficiently with state-of-the-art solvers. Convex problems are formulated as regularized least-squares, second-order cone programming, and weighted L1-norm minimization problems. In PP based methods, SPFs that entail rich optimization properties are employed. Recovery is achieved by iteratively performing two fundamental operations, namely, computation of the PP of the SPF and projection of the PP onto a convex set. The first operation is performed analytically or numerically by using a fast iterative method. The second operation is performed efficiently by computing a sequence of closed-form projectors. The proposed methods have been compared with the leading state-of-the-art signal-recovery methods, namely, the gradient-projection method of Figueiredo, Nowak, and Wright, the L1-LS method of Kim, Koh, Lustig, Boyd, and Gorinevsky, the L1-Magic method of Candes and Romberg, the spectral projected-gradient L1-norm method of Berg and Friedlander, the iteratively reweighted least squares method of Chartrand and Yin, the difference-of-two-convex-functions method of Gasso, Rakotomamonjy, and Canu, and the NESTA method of Becker, Bobin, and Candes. The comparisons concerned the capability of the proposed and competing algorithms in recovering signals in a wide range of test problems and also the computational efficiency of the various algorithms. Simulation results demonstrate that improved reconstruction performance, measurement consistency, and comparable computational cost are achieved with the proposed methods relative to the competing methods. The proposed methods are robust, are supported by known convergence theorems, and lead to fast convergence. They are, as a consequence, particularly suitable for the solution of hard recovery problems of large size that entail large dynamic range and, are, in effect, strong candidates for use in many real-world applications. / Graduate / 0544 / eng.flavio.teixeira@gmail.com

Thesis advisor: Willie J. Padilla / This thesis will describe the implementation of novel imaging applications with electromagnetic metamaterials. Metamaterials have proven to be host to a multitude of interesting physical phenomena and give rich insight electromagnetic theory. This thesis will explore not only the physical theory that give them their interesting electromagnetic properties, but also the many applications of metamaterials. There is a strong need for efficient, low cost imaging solutions, specifically in the longer wavelength regime. While this technology has often been at a standstill due to the lack of natural materials that can effectively operate at these wavelengths, metamaterials have revolutionized the creation of devices to fit these needs. Their scalability has allowed them to access regimes of the electromagnetic spectrum previously unobtainable with natural materials. Along with metamaterials, mathematical techniques can be utilized to make these imaging systems streamlined and effective. Chapter 1 gives a background not only to metamaterials, but also details several parts of general electromagnetic theory that are important for the understanding of metamaterial theory. Chapter 2 discusses one of the most ubiquitous types of metamaterials, the metamaterial absorber, examining not only its physical mechanism, but also its role in metamaterial devices. Chapter 3 gives a theoretical background of imaging at longer wavelengths, specifically single pixel imaging. Chapter 3 also discusses the theory of Compressive Sensing, a mathematical construct that has allowed sampling rates that can exceed the Nyquist Limit. Chapter 4 discusses work that utilizes photoexcitation of a semiconductor to modulate THz radiation. These physical methods were used to create a dynamic THz spatial light modulator and implemented in a single pixel imaging system in the THz regime. Chapter 5 examines active metamaterial modulation through depletion of carriers in a doped semiconductor via application of a bias voltage and its implementation into a similar single pixel imaging system. Additionally, novel techniques are used to access masks generally unobtainable by traditional single pixel imagers. Chapter 6 discusses a completely novel way to encode spatial masks in frequency, rather than time, to create a completely passive millimeter wave imager. Chapter 7 details the use of telecommunication techniques in a novel way to reduce image acquisition time and further streamline the THz single pixel imager. Finally, Chapter 8 will discuss some future outlooks and draw some conclusions from the work that has been done. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

A nonogram is a logic puzzle where one shades certain cells of a 2D grid to reveal a hidden image. One uses the sequences of numbers on the left and the top of the grid to figure out how many and which cells to shade. We propose a new technique to solve a nonogram using compressive sensing. Our method avoids (1) partial fill-ins, (2) heuristics, and (3) over-complication, and only requires that we solve a binary integer programming problem. / text

This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property. / <p>QC 20140228</p>

Dissertação (mestrado)—Universidade de Brasília, Faculdade Gama, Programa de Pós-Graduação em Engenharia Biomédica, 2017. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2017-05-03T17:41:24Z No. of bitstreams: 1 2017_DanielLucasFerreiraeAlmeida.pdf: 15210206 bytes, checksum: df62328627085f382c7eff9dbdf98b0f (MD5) / Approved for entry into archive by Raquel Viana (raquelviana@bce.unb.br) on 2017-09-11T16:40:09Z (GMT) No. of bitstreams: 1 2017_DanielLucasFerreiraeAlmeida.pdf: 15210206 bytes, checksum: df62328627085f382c7eff9dbdf98b0f (MD5) / Made available in DSpace on 2017-09-11T16:40:09Z (GMT). No. of bitstreams: 1 2017_DanielLucasFerreiraeAlmeida.pdf: 15210206 bytes, checksum: df62328627085f382c7eff9dbdf98b0f (MD5) Previous issue date: 2017-09-11 / A utilização de imagens obtidas por meio da ressonância magnética (do inglês magneticresonance, ou MR) auxilia no diagnóstico e no acompanhamento das mais diversas patologias que afetam o corpo humano. Ela apresenta, contudo, um custo mais elevado do que outras técnicas de imageamento que não são capazes de gerar imagens com a mesma qualidade objetiva, e isso pode dificultar o trabalho dos profissionais de saúde. Esse custo mais elevado se deve ao alto valor do equipamento e de sua manutenção, bem como ao baixo número de exames que podem ser realizados por dia, quando comparados com os de técnicas como a tomografia computadorizada. Além de seu processo de aquisição ser inerentemente mais lento, uma vez que sua duração depende da alta quantidade de medidas extraídas pelo scanner. De modo a diminuir a quantidade de medidas necessária, técnicas de reconstrução alternativas às tradicionais vêm sendo estudadas, como as que se baseiam em compressive sensing (CS). O CS permite reconstruir um sinal a partir de uma quantidade de medidas muito inferior `a estabelecida pelo critério de Nyquist. Além disso, o imageamento por ressonância magnética atende aos requisitos mínimos para a aplicação dessa técnica: o sinal possui uma representação esparsa num domínio transformado e as medidas adquiridas pelo scanner já são naturalmente codificadas. Essas técnicas têm sido eficientes ao diminuir a quantidade de medidas e garantir uma boa qualidade objetiva da imagem reconstruída, mas ainda há potencial para que essa diminuição seja maior. Uma das alternativas é encontrar a transformada esparsificante que torne o sinal o mais esparso possível, como a transformada de Fourier bidimensional, transformadas baseadas em wavelets e a pré-filtragem. Além disso, a utilização de informação a priori aliada aos algoritmos de reconstrução que se baseiam em compressive sensing também é utilizada para diminuir a quantidade de medidas. Essa informação pode ser caracterizada por dados estatísticos prévios da imagem ou com base em informações determinísticas sobre ela. Neste trabalho, propomos uma modelagem estocástica da informação a priori a ser utilizada em algoritmos de reconstrução de imagens de ressonância magnéticas baseados em compressive sensing com pré-filtragem. Nossa abordagem gera um espalhamento probabilístico em torno de um ponto que apresenta o potencial de pertencer ao suporte da versão esparsa da imagem a ser reconstruída. Esse espalhamento proposto tem o objetivo de garantir que a imagem possa ser reconstruída, mesmo em situações nas quais o ponto do suporte pode mudar de posição – quando um paciente se movimenta dentro do scanner, por exemplo. De modo a validar essa técnica, n´os a aplicamos a sinais de domínio unidimensional, bidimensional, imagens de fantomas de Shepp-Logan e imagens reais de RM. Os resultados dos testes sistemáticos em sinais de domínio unidimensional mostram que essa abordagem estocástica apresenta melhores resultados de reconstrução do que aquele que não utiliza informação a priori, apresentando um SER superior em cerca de 100dB para alguns valores de medidas ℓ. Em sinais de domínio bidimensional e de fantomas, apresentamos os resultados de um estudo de caso envolvendo a reconstrução de um sinal de cada tipo. Os resultados corroboram o que foi encontrado com os sinais de domínio unidimensional, com a abordagem estocástica apresentado valores de SER superiores em cerca de 10dB quando comparada com a abordagem determinística, apesar da pouca significância estatística. Os testes em imagens de MR incluíram a reconstrução de imagens deslocadas para simular uma possível situação de movimento do paciente durante a aquisição do exame. Além disso, foi analisada a influência do número de linhas radiais na reconstrução, bem como da matriz de covariância usada para gerar a função de espalhamento. Os resultados mostram que a abordagem estocástica apresenta sempre um bom desempenho quando comparada com as demais e, muitas vezes, esse desempenho é superior ao das outras técnicas. Em alguns pontos críticos, por exemplo, o valor do SER para a abordagem estocástica chega a ser superior em 6dB com relação ao caso ideal e em mais de 10dB para o caso não-ideal. Algo importante de se destacar é o fato de a abordagem estocástica apresentar um bom desempenho constantemente (um valor médio de SER de 21dB e do índice SSIM de 0,7), inclusive em casos em que as demais falham. Os resultados encontrados permitem agora que outras formas de explorar essa informação a priori possam ser investigados, para diminuir ainda mais a quantidade de medidas necessária para a reconstrução. Mas é também importante realizar um estudo teórico para quantificar a probabilidade de reconstrução em função da representação estocástica da informação a priori e da quantidade de medidas disponível. / The use of images obtained through MRI helps in the diagnosis and follow-up of the most diverse pathologies that affect the human body. However, it presents a higher cost than other imaging techniques that are not capable of generating images with the same objective quality, and this may hinder the work of health professionals. This higher cost is due to the high value of the equipment and its maintenance, as well as to the low number of tests that can be carried out per day, when compared to techniques such as the computed tomography. Besides its acquisition process is inherently slower, since its duration depends on the high amount of measurements extracted by the scanner. In order to reduce the amount of measurements required, alternatives to traditional reconstruction techniques have been studied, such as those based on compressive sensing. The CS allows you to reconstruct a signal from a quantity of measures much lower than the one established by the Nyquist theorem. In addition, magnetic resonance imaging meets the minimum requirements for the application of this technique: the signal has a sparse representation in a transformed domain and the measurements acquired by the scanner are already encoded naturally. These techniques have been effective in decreasing the number of measurements and ensuring a good objective quality of the reconstructed image, but there is still potential for such a decrease. One of the alternatives is to find a sparsifying transform that makes the signal as sparse as possible, such as the two-dimensional Fourier transform, wavelet-based transforms, and pre-filtering. Besides, the use of a prior information coupled with reconstruction algorithms based on compressive sensing is also used to decrease the number of measurements. This information may be characterized by prior statistical data of the image or based on deterministic information about it. In this work, we propose a stochastic modeling of the prior information to be used in reconstruction algorithms of magnetic resonance images based on compressive sensing with pre-filtering. Our approach generates a probabilistic spreading around a point that has the potential to belong to the support of the sparse version of the image to be reconstructed. This proposed spread is intended to ensure that the image can be reconstructed, even in situations when the position of the support point may change - when a patient moves within the scanner, for example. In order to validate this technique, we apply it to one-dimensional, two-dimensional domain signals, Shepp-Logan phantom images, and real MRI images. The results of the systematic tests on one-dimensional domain signals show that this stochastic approach presents better reconstruction results than those that do not use the prior information, with a SER 100dB greater for some number of measures ℓ. In two-dimensional domain signals and phantoms, we present the results of a case study involving the reconstruction of a signal of each type. The results corroborate what was found with one-dimensional domain signals, with the SER for the stochastic approach being 10dB higher than when the deterministic approach was used, despite the low statistical significance. The MR imaging tests included the reconstruction of shifted images to simulate a possible patient movement situation during the acquisition of the examination. In addition, the influence of the number of radial lines in the reconstruction was analyzed, as well as the covariance matrix used to generate the spreading function. The results show that the stochastic approach always performs well when compared to the others, and this performance is often superior to other techniques. When considering some critic points, for instance, the SER value for the stochastic approach is 6dB higher than the ideal prior approach, and more than 10dB higher than the non-ideal. Something important to emphasize is that the stochastic approach performs consistently well (a SER mean value of around 21dB and a SSIM index of around 0,7), even when the others fail. Those results will now allow the investigation of other ways to explore this prior information in order to further reduce the amount of measures required for reconstruction. But it is also important to carry out a theoretical study to quantify the reconstruction probability as a function of the stochastic representation of the prior information and of the quantity of measures available.

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Programa de Pós-Graduação em Engenharia Biomédica, 2017. / Submitted by Raquel Almeida (raquel.df13@gmail.com) on 2017-11-14T16:22:17Z No. of bitstreams: 1 2017_GianLucasdeOliveiraPaiva.pdf: 4207150 bytes, checksum: aa6048e4656a7ed3af0aef65ac9f3311 (MD5) / Approved for entry into archive by Raquel Viana (raquelviana@bce.unb.br) on 2017-11-21T18:35:34Z (GMT) No. of bitstreams: 1 2017_GianLucasdeOliveiraPaiva.pdf: 4207150 bytes, checksum: aa6048e4656a7ed3af0aef65ac9f3311 (MD5) / Made available in DSpace on 2017-11-21T18:35:34Z (GMT). No. of bitstreams: 1 2017_GianLucasdeOliveiraPaiva.pdf: 4207150 bytes, checksum: aa6048e4656a7ed3af0aef65ac9f3311 (MD5) Previous issue date: 2017-11-21 / O imageamento por ressonância magnética (RM) constitui uma das várias modalidades de imagens médicas utilizadas para diagnóstico, acompanhamento de doenças e planejamento de tratamentos. Ela é capaz de produzir imagens com melhor contraste, além de não emitir radiação ionizante, o que a torna uma escolha atraente para exames. Entretanto, seu maior custo e tempo de exame dificultam o seu uso de maneira mais generalizada. Reduzir o tempo de exame tem se tornado um importante tema de pesquisa na área de processamento de sinais nos últimos anos. Compressive Sensing é uma técnica que tem sido utilizada em vários estudos de ressonância magnética. O seu uso com transformadas esparsificantes abre uma grande variedade de possibilidades com o uso de filtros sobre as informações da imagem. Transformadas comuns utilizadas em ressonância magnética e compressive sensing são as wavelets. Um tipo de wavelet pouco explorado em ressonância magnética é a transformada wavelet dualtree, que possui algumas vantagens sobre a wavelet comum. Neste trabalho é feita a hipótese de que a transformada wavelet dualtree é superior às transformadas wavelet comuns pela possibilidade de esparsificar melhor, devido a maior seletividade de direções para imagens. Foram utilizados bancos de filtros para implementação das transformadas e também como método de reconstrução das imagens pré-filtradas, reconstruídas por compressive sensing. O banco de filtros foi comparado com o método de recomposição espectral usando métricas de qualidade objetiva (SNR e SSIM). Os métodos também foram comparados em relação ao tempo de reconstrução. Filtros de diferentes tipos e famílias foram comparados entre si, utilizando banco de filtros como método de reconstrução. Um conjunto de 73 imagens de cabeça foi utilizado para avaliar estatisticamente os resultados, para verificar se a diferença na qualidade das imagens por filtros diferentes é estatisticamente significante. Os resultados indicaram que, para os filtros de Haar, o método de recomposição espectral foi superior ao método do banco de filtros, com diferenças entre valores da SNR chegando a 14 dB e 0.1 para o SSIM para uma mesma imagem, em um nível. O filtro dtf4 em dois níveis obteve qualidade semelhantes para ambos os métodos de banco de filtros e a recomposição espectral. Foi observado que o banco de filtros obteve uma melhora na qualidade com o aumento de níveis de decomposição, enquanto a recomposição espectral foi quase insensível ao aumento de níveis, apresentando apenas uma ligeira melhora na qualidade do primeiro nível para o segundo. A comparação objetiva entre diferentes filtros, utilizando o banco de filtros como método de reconstrução, mostrou que os quatro filtros dualtree, em todos os casos, obtiveram resultados significantemente melhores que os outros filtros wavelet, com valores médios de SNR até 3 dB maiores que os outros filtros. A família de filtros coiflets apresentou, na média, resultados próximos aos dos filtros dualtree. Os filtros biortogonais reversos 3.1 e 3.3 apresentaram os piores resultados, seguidos dos filtros Daubechies/symlet 1 e 2, biortogonal e biortogonal reverso 1.1 e 1.5. Os tempos de recomposição para o banco de filtros foram menores que os tempos da recomposição espectral, chegando a ser 30 vezes menores, embora esse tempo seja praticamente desprezível em relação ao tempo total de reconstrução da imagem. Concluiu-se que o método do banco de filtros, utilizando os filtros dualtree, permite a reconstrução de imagens com qualidade semelhante ao do método de recomposição espectral, com tempos menores de recomposição e utilizando a mesma quantidade de informação. Os filtros dualtree também se mostraram superiores aos filtros wavelet comuns para o uso com banco de filtros. / Magnetic resonance imaging (MRI) is one of several medical imaging modalities used for diagnosis, disease monitoring and treatment planning. It is able to produce images with better contrast, besides not emitting ionizing radiation, which makes it an attractive choice for exams. However, its higher cost and time of examination make it more difficult to use. Reducing exam time has become an important research topic in the area of signal processing in recent years. Compressive sensing is a technique that has been used in several magnetic resonance studies. Its use with sparse transforms opens a wide range of possibilities with the use of filters over the image information. Common transforms used in magnetic resonance imaging and compressive sensing are the wavelets. A type of wavelet not thoroughly explored on MRI is the dualtree wavelet transform, which has some advantages over the common wavelet. In this work, it is hypothesized that the dualtree wavelet transform is superior to the ordinary wavelets due to the possibility of better scattering, thanks to its greater directionalities for images. Filter banks were used to implement the transforms and also as a method of reconstructing the prefiltered images, recovered by compressive sensing. The filter bank was compared to the spectral recomposition method using objective quality metrics (SNR and SSIM). The methods were also compared to in relation to the reconstruction time. Filters of different types and families were compared to each other, using filter bank as reconstruction method. A set of 73 MRI head imaged was used to statistically evaluate the results, to verify if the difference in the image quality recovered using different filters is statistically significant. The results indicated that, for the Haar filters, the spectral recomposition method was superior to the filter bank method, with differences between SNR values reaching up to 14 dB and 0.1 for SSIM for the same image at one level of decomposition. The twolevel decomposition dtf4 filter obtained similar quality for both filterbank methods and spectral recomposition. It was observed that the filter bank obtained an improvement in quality with increasing decomposition levels, while the spectral recomposition was almost insensitive to the increase of levels, presenting only a slight improvement in quality from the first level to the second. The objective comparison of different filters using the filter bank as a reconstruction method showed that the four dualtree filters, in all cases, obtained significantly better results than the other wavelet filters with mean values of SNR up to 3 dB higher than the other filters. The coiflet family of filters presented, on average, results close to the dualtree filters. The reverse biorthogonal filters 3.1 and 3.3 had the worst results, followed by the Haar filter and reverse biorthogonal filters 1.3 and 1.5. The recomposition times for the filter bank were smaller than that of spectral recomposition, being up to 30 times faster. although this times is negligible in relation to the total times of reconstruction of the image. It was concluded that the filter bank method, using the dualtree filters, allows the reconstruction of images with similar quality to the spectral recomopsition, with smaller recomposition times and using the same amount of information. The dualtree filters were also shown to be superior to the common wavelet filters using filter bank.

A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas. / Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.

A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas. / Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.