In this thesis, we investigate the application of compressive sensing and sparse signal processing techniques to image compression and inpainting problems. Considering that many signals are sparse in certain transformation domain, a natural question to ask is: can an image be represented by as few coefficients as possible? In this thesis, we propose a new model for image compression/decompression based on sparse representation. We suggest constructing an overcomplete dictionary by combining two compression matrices, the discrete cosine transform (DCT) matrix and Hadamard-Walsh transform (HWT) matrix, instead of using only one transformation matrix that has been used by the common compression techniques such as JPEG and JPEG2000. We analyze the Structural Similarity Index (SSIM) versus the number of coefficients, measured by the Normalized Sparse Coefficient Rate (NSCR) for our approach. We observe that using the same NSCR, SSIM for images compressed using the proposed approach is between 4%-17% higher than when using JPEG. Several algorithms have been used for sparse coding. Based on experimental results, Orthogonal Matching Pursuit (OMP) is proved to be the most efficient algorithm in terms of computational time and the quality of the decompressed image. In addition, based on compressive sensing techniques, we propose an image inpainting approach, which could be used to fill missing pixels and reconstruct damaged images. In this approach, we use the Gradient Projection for Sparse Reconstruction (GPSR) algorithm and wavelet transformation with Daubechies filters to reconstruct the damaged images based on the information available in the original image. Experimental results show that our approach outperforms existing image inpainting techniques in terms of computational time with reasonably good image reconstruction performance.

Este estudo objetivou avaliar a resistência máxima às forças de compressão entre dois grupos diferentes de coroas em porcelanas livres de metal cimentadas sobre dentes naturais e um grupo formado por dentes caninos naturais hígidos e comparar os resultados obtidos com os de (Chaves, 2001), em seu trabalho de Doutorado onde também se avaliou a resistência máxima às forças de compressão entre coroa metalo cerâmica fraturada e reparada com resina composta com coroa metalo cerâmica integra e dente natural permanente. No presente estudo foram feitos vinte preparos para coroa total em dentes naturais caninos e divididos em dois grupos para confecção de dez coroas do sistema cerâmico aluminizado infiltrado por vidro (Angelus Brasil) e dez coroas em porcelana feldspática Noritake ® (Noritake Kisai CO. Cada grupo de coroas foi cimentado com cimento resinoso auto adesivo RelyX Unicem ® , (3M ESPE, Brasil) com o objetivo de aumentar a resistência da porcelana frente às forças de compressão. O teste de compressão foi realizado em uma máquina de ensaio universal KRATOS, através de uma carga aplicada axialmente no ápice da borda incisal de cada espécime até a fratura. Os dados foram submetidos à análise de Variância ANOVA (p < 0,05) e teste de Tukey para comparação entre grupos. Os resultados mostraram que não houve diferença estatisticamente significante entre a coroa de porcelana aluminizada infiltrada por vidro e o dente natural. A coroa de porcelana feldspática apresentou-se menos resistente com relação ao dente natural e coroa de porcelana aluminizada infiltrada por vidro. / The objective of this study is evaluate the maximum load resistance between two different groups of porcelain metal free crown seated on natural teeth and a group of natural canine and to compare the results gotten with the ones of (Chaves, 2001), in its work of Doutorado where also the ultimate strength to the forces of compression between metalo ceramic broken and repaired with composite resin with ceramic crown metaloceramic integrates and permanent natural tooth. In the present study twenty natural canine teeth were prepared for crown canines and divided in two groups: aluminized porcelain crown infiltrated for glass (Angelus Brazil) and feldspathic Noritake Kisai Noritake (co). Crowns were seated using self adhesive resin cement RelyX Unicem (3M ESPE, Brazil) Compression testing was performed by a universal testing machine (KRATOS) by a load applied axially in incisal of each specimen until occurs the fracture. The data were analyzed by one way analyses of variance (ANOVA) and Tukey test for comparison between groups. The results showed that it did not have statistical significant difference between aluminized porcelain crown infiltrated by glass and natural tooth. The feldspathic porcelain crown presented less resistant than natural tooth and aluminized porcelain crown infiltrated by glass. .

With the rising of new paradigms in wireless communications such as Internet of things (IoT), current static frequency allocation policy faces a primary challenge of spectrum scarcity, and thus encourages the IoT devices to have cognitive capabilities to access the underutilised spectrum in the temporal and spatial dimensions. Wideband spectrum sensing is one of the key functions to enable dynamic spectrum access, but entails a major implementation challenge in terms of sampling rate and computation cost since the sampling rate of analog-to-digital converters (ADCs) should be higher than twice of the spectrum bandwidth based on the Nyquist-Shannon sampling theorem. By exploiting the sparse nature of wideband spectrum, sub-Nyquist sampling and sparse signal recovery have shown potential capabilities in handling these problems, which are directly related to compressive sensing (CS) from the viewpoint of its origin. To invoke sub-Nyquist wideband spectrum sensing in IoT, blind signal acquisition with low-complexity sparse recovery is desirable on compact IoT devices. Moreover, with cooperation among distributed IoT devices, the complexity of sampling and reconstruc- tion can be further reduced with performance guarantee. Specifically, an adaptively- regularized iterative reweighted least squares (AR-IRLS) reconstruction algorithm is proposed to speed up the convergence of reconstruction with less number of iterations. Furthermore, a low-complexity compressive spectrum sensing algorithm is proposed to reduce computation complexity in each iteration of IRLS-based reconstruction algorithm, from cubic time to linear time. Besides, to transfer computation burden from the IoT devices to the core network, a joint iterative reweighted sparse recovery scheme with geo-location database is proposed to adopt the occupied channel information from geo- location database to reduce the complexity in the signal reconstruction. Since numerous IoT devices access or release the spectrum randomly, the sparsity levels of wideband spec-trum signals are varying and unknown. A blind CS-based sensing algorithm is proposed to enable the local secondary users (SUs) to adaptively adjust the sensing time or sam- pling rate without knowledge of spectral sparsity. Apart from the signal reconstruction at the back-end, a distributed sub-Nyquist sensing scheme is proposed by utilizing the surrounding IoT devices to jointly sample the spectrum based on the multi-coset sam- pling theory, in which only the minimum number of low-rate ADCs on the IoT devices are required to form coset samplers without the prior knowledge of the number of occu- pied channels and signal-to-noise ratios. The models of the proposed algorithms are derived and verified by numerical analyses and tested on both real-world and simulated TV white space signals.

Two efficient models in two-dimensional signal processing are proposed in the thesis. The first model deals with large scale spectral compressive sensing in continuous domain, which aims to recover a 2D spectrally sparse signal from partially observed time samples. The signal is assumed to be a superposition of s complex sinusoids. We propose a semidefinite program for the 2D signal recovery problem. Our model is able to handle large scale 2D signals of size 500*500, whereas traditional approaches only handle signals of size around 20*20. The second model deals with the problem of single image reflection suppression. Removing the undesired reflection from images taken through glass is of great importance in computer vision. It serves as a means to enhance the image quality for aesthetic purposes as well as to preprocess images in machine learning and pattern recognition applications. We propose a convex model to suppress the reflection from a single input image. Our model implies a partial differential equation with gradient thresholding, which is solved efficiently using Discrete Cosine Transform. Extensive experiments on synthetic and real-world images demonstrate that our approach achieves desirable reflection suppression results and dramatically reduces the execution time compared to the state of the art.

Two-dimensional infrared spectroscopy (2D IR) is a powerful tool to investigate molecular structures and dynamics on femtosecond to picosecond time scales and is applied to diverse systems. Current technologies allow for the acquisition of a single 2D IR spectrum in a few hundreds of milliseconds using a pulse shaper and an array detector, but demanding applications require spectra for many waiting times and involve considerable signal averaging, resulting in data acquisition times that can be many days of laboratory measurement time. Compressive sampling is an emerging signal processing technique to reduce data acquisition time in diverse fields by requiring only a fraction of the traditional number of measurements while yielding much of the same information as the fully-sampled data. Here we combine cutting-edge 2D IR methodology with a novel compressive sampling reconstruction algorithm to reduce the data acquisition time of 2D IR spectroscopy without distorting lineshapes. We introduce the Generic Iteratively Reweighted Annihilating Filter (GIRAF) algorithm re-engineered to the specific problem of 2D IR reconstruction and show its effectiveness applied to various systems, including those with low signal, with multiple peaks, and with differing amounts of frequency shifting. Additionally, we lay the groundwork for 2D IR microscopic imaging using compressive sampling in the spatial image domain. The first instance of a single-pixel camera in the infrared is introduced.

This in vitro study evaluated the bond and compression strength of cemented leucite reinforced glass ceramics in bovine tooth enamel, comparing three etching times with hydrofluoric acid 10% of the ceramic surface (20, 60 and 90 seconds) and two adhesive treatments (adhesive system + silane and universal adhesive system). For the bond strength test, 120 ceramic cylinders (2mm diameter x 2mm length; n=20) were etched and cemented (80m thick) in enamel with a dual resin cement, varying the adhesive treatment, obtaining the groups: UEXC20s, UEXC60s, UEXC90s, USBU20s, USBU60s, USBU90s. After 24 hours, the shear bond strength test was performed on a universal test machine (0.5mm/min, 50kgf). For the compression test, 30 ceramic plates (5x5mm with 1mm thick, n=5) were etched, received the same adhesive treatments and were cemented (80m) in enamel, obtaining the following groups: CEXC20s, CEXC60s, CEXC90s, CSBU20s, CSBU60s, CSBU90s. After 24 hours of cementation, the compression test (0.5mm/min, 500kgf) was performed. Statistical analysis was performed using two-way ANOVA and Tukey test (=.05). For the shear bond strength test significant differences were found among the adhesives (p<.05). For the etching times there were no differences (p=.059). However, there was a significant interaction between the adhesives and the etching times (p=.021). At 60 seconds, the Silane + ExciTE F DSC Adhesive presented the highest bond strength values (47.53±16.70Mpa). And at 20 seconds, the Universal adhesive presented the lowest bond strength values (27.72±10.76Mpa). For the compression test there were no significant differences between the adhesives (p=.571) and between the times (p=.154). The group that presented the highest values of compression force was the Universal adhesive at 60 seconds (1757.89±200.47N). The lowest values were also the Universal adhesive, but at 90 seconds (1213.30±546.34N). The study concluded that the silane associated with the ExciTE F DSC adhesive showed the highest bond strength values at the etching time of 60 seconds with 10% hydrofluoric acid, without compromising the compressive strength of the leucite reinforced ceramic. / Este estudo in vitro avaliou a resistência de união e compressão da cerâmica reforçada por cimentada em esmalte de dentes bovinos, comparando-se três tempos de condicionamento com ácido fluorídrico 10% da superfície cerâmica (20, 60 e 90 segundos) e dois tratamentos adesivos (sistema adesivo + silano e sistema adesivo universal). Para o teste de resistência de união (U), 120 cilindros cerâmicos (2mm diâmetro x 2mm comprimento; n=20) foram condicionados e cimentados (80 m de espessura) em esmalte, com cimento resinoso dual, variando-se o tratamento adesivo, obtendo-se os grupos: UEXC20s, UEXC60s, UEXC90s, USBU20s, USBU60s, USBU90s. Após 24h, foi realizado o teste de cisalhamento (0,5mm/min, 50kgf). Para o teste de compressão (C), 30 placas cerâmicas (5x5mm com 1mm de espessura; n=5) foram condicionadas, receberam os mesmos tratamentos adesivos e foram cimentadas (80m) em esmalte, obtendo-se os grupos: CEXC20s, CEXC60s, CEXC90s, CSBU20s, CSBU60s, CSBU90s. Após 24h da cimentação, foi realizado o teste de compressão (0,5mm/min, 500kgf). Foi realizada a análise estatística por meio de ANOVA dois critérios e teste de Tukey (P < 0,05). Para o teste de cisalhamento diferenças significativas foram encontradas entre os adesivos (p<0,05). Para os tempos de condicionamento não houve diferenças significativas (p=0,059). No entanto, houve interação significativa entre os adesivos e os tempos de condicionamento (p=0,021). No tempo de 60 segundos, o silano + adesivo ExciTE F DSC apresentou os maiores valores de resistência de união (47,53±16,70Mpa). E no tempo de 20 segundos, o adesivo Universal apresentou os menores valores de resistência de união (27,72±10,76Mpa). Para o teste de compressão não houve diferenças significativas entre os adesivos (p=0,571) e entre os tempos (p=0,154). O grupo que apresentou maiores valores de força de compressão foi o adesivo Universal no tempo de 60 segundos (1757,89±200,47N). Já os menores valores, foi também o adesivo Universal, mas no tempo de 90 segundos (1213,30±546,34N). Pode-se concluir que, o Silano associado ao adesivo ExciTE F DSC, mostrou os maiores valores de resistência de união no tempo de condicionamento de 60 segundos com ácido fluorídrico a 10%, sem comprometer a resistência a compressão da cerâmica reforçada por leucita.

In this study, trabecular architecture is considered as a cellular solid structure, including both intact and damaged bone models. ??Intact?? bone models were constructed based on ideal versions of 25, 60 and 80-year-old specimens with varying trabecular lengths and orientations to 5%, and 10% covariance of variation (COV). The models were also flipped between longer transverse and longer longitudinal trabeculae. With increasing COV of lengths and orientations of trabecular bone, the apparent modulus is linearly decreased, especially in the longer transverse trabeculae lengths. ??Damaged?? bone models were built from the 25 year old model at 5% COV of longer transverse trabeculae, and with removing trabeculae of 5% and 10% of trabecular volume in transverse and longitudinal directions, respectively, as well as in combination to total 10% and 15%. With increasing percent of trabeculae missing, the apparent modulus decreased, especially dramatically when removal was only in the transverse direction. The trabecular bone models were also connected to a cortical shell and it was found that the apparent modulus of an entire slice was increased in comparison to the modulus of trabecular bone alone. We concluded that the architecture of trabecular bone, especially both lengths and percent of trabecular missing in the longitudinal direction, significantly influences mechanical properties.

Compressive sensing (CS) is a new sampling theory which allows reconstructing signals using sub-Nyquist measurements. It states that a signal can be recovered exactly from randomly undersampled data points if the signal exhibits sparsity in some transform domain (wavelet, Fourier, etc). Instead of measuring it uniformly in a local scheme, signal is correlated with a series of sensing waveforms. These waveforms are so called sensing matrix or measurement matrix. Every measurement is a linear combination of randomly picked signal components. By applying a nonlinear convex optimization algorithm, the original can be recovered. Therefore, signal acquisition and compression are realized simultaneously and the amount of information to be processed is considerably reduced. Due to its unique sensing and reconstruction mechanism, CS creates a new situation in signal acquisition hardware design as well as software development, to handle the increasing pressure on imaging sensors for sensing modalities beyond visible (ultraviolet, infrared, terahertz etc.) and algorithms to accommodate demands for higher-dimensional datasets (hyperspectral or video data cubes). The combination of CS with traditional optical imaging extends the capabilities and also improves the performance of existing equipments and systems. Our research work is focused on the direct application of compressive sensing for imaging in both 2D and 3D cases, such as infrared imaging, hyperspectral imaging and sum frequency generation microscopy. Data acquisition and compression are combined into one step. The computational complexity is passed to the receiving end, which always contains sufficient computer processing power. The sensing stage requirement is pushed to the simplest and cheapest level. In short, simple optical engine structure, robust measuring method and high speed acquisition make compressive sensing-based imaging system a strong competitor to the traditional one. These applications have and will benefit our lives in a deeper and wider way.

Wide-band spectrum sensing is an approach for finding spectrum holes within a wideband signal with less complexity/delay than the conventional approaches. In this thesis, we propose four different algorithms for detecting the holes in a wide-band spectrum and finding the sparsity level of compressive signals. The first algorithm estimates the spectrum in an efficient manner and uses this estimation to find the holes. The second algorithm detects the spectrum holes by reconstructing channel energies instead of reconstructing the spectrum itself. In this method, the signal is fed into a number of filters. The energies of the filter outputs are used as the compressed measurement to reconstruct the signal energy. The third algorithm employs two information theoretic algorithms to find the sparsity level of a compressive signal and the last algorithm employs belief propagation for detecting the sparsity level.

Wide-band spectrum sensing is an approach for finding spectrum holes within a wideband signal with less complexity/delay than the conventional approaches. In this thesis, we propose four different algorithms for detecting the holes in a wide-band spectrum and finding the sparsity level of compressive signals. The first algorithm estimates the spectrum in an efficient manner and uses this estimation to find the holes. The second algorithm detects the spectrum holes by reconstructing channel energies instead of reconstructing the spectrum itself. In this method, the signal is fed into a number of filters. The energies of the filter outputs are used as the compressed measurement to reconstruct the signal energy. The third algorithm employs two information theoretic algorithms to find the sparsity level of a compressive signal and the last algorithm employs belief propagation for detecting the sparsity level.