Digital Filter Design Using Improved Teaching-Learning-Based Optimization

Digital filters are an important part of digital signal processing systems. Digital filters are divided into finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters according to the length of their impulse responses. An FIR digital filter is easier to implement than an IIR digital filter because of its linear phase and stability properties. In terms of the stability of an IIR digital filter, the poles generated in the denominator are subject to stability constraints. In addition, a digital filter can be categorized as one-dimensional or multi-dimensional digital filters according to the dimensions of the signal to be processed. However, for the design of IIR digital filters, traditional design methods have the disadvantages of easy to fall into a local optimum and slow convergence. The Teaching-Learning-Based optimization (TLBO) algorithm has been proven beneficial in a wide range of engineering applications. To this end, this dissertation focusses on using TLBO and its improved algorithms to design five types of digital filters, which include linear phase FIR digital filters, multiobjective general FIR digital filters, multiobjective IIR digital filters, two-dimensional (2-D) linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters. Among them, linear phase FIR digital filters, 2-D linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters use single-objective type of TLBO algorithms to optimize; multiobjective general FIR digital filters use multiobjective non-dominated TLBO (MOTLBO) algorithm to optimize; and multiobjective IIR digital filters use MOTLBO with Euclidean distance to optimize. The design results of the five types of filter designs are compared to those obtained by other state-of-the-art design methods. In this dissertation, two major improvements are proposed to enhance the performance of the standard TLBO algorithm. The first improvement is to apply a gradient-based learning to replace the TLBO learner phase to reduce approximation error(s) and CPU time without sacrificing design accuracy for linear phase FIR digital filter design. The second improvement is to incorporate Manhattan distance to simplify the procedure of the multiobjective non-dominated TLBO (MOTLBO) algorithm for general FIR digital filter design. The design results obtained by the two improvements have demonstrated their efficiency and effectiveness

Uma nova abordagem para o uso de métodos diretos na reconstrução de imagens médicas com compressive sensing

Dissertação (mestrado) — Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2022.A partir das tecnologias de imageamento médico, profissionais de saúde conseguem informações relevantes sobre o estado de um paciente para o planejamento e acompanhamento de seu tratamento. A Tomografia Computadorizada por raios-x (CT) e a Ressonância Magnética (MR) são duas das tecnologias mais bem consolidadas no meio. Estas técnicas permitem a obtenção de imagens anatômicas de planos específicos ou volumes. Apesar de a CT e a MR explorarem princípios físicos diferentes, ambas coletam medidas que podem ser modeladas como coeficientes da Transformada de Fourier da imagem a ser reconstruída. O processo de reconstrução refere-se a etapa de calcular a imagem desejada a partir das medidas adquiridas pelos equipamentos médicos. A aquisição geralmente requer que o paciente permaneça em uma mesma posição por longos períodos e, no caso da CT, há a emissão de radiação ionizante. Assim, é de interesse que tais procedimentos ocorram da forma mais segura e rápida possível. Uma maneira de abordar este problema é o desenvolvimento de algoritmos de reconstrução que consigam gerar imagens úteis para a atividade clínica usando uma quantidade reduzida de medidas. Conceitos de Compressive Sensing (CS) vem sendo adotados na elaboração de novos algoritmos para reconstrução de imagens médicas em vista de uma aquisição mais eficiente. Esta área de conhecimento estuda a reconstrução de sinais a partir de medidas incompletas por meio da resolução de sistemas lineares subdeterminados. O sinal de interesse é a solução cuja maior parte dos coeficientes é nula. Ou seja, considera-se que o sinal reconstruído possui uma representação esparsa em algum domínio conhecido. A minimização de `p (0 < p ≤ 1) é uma estratégia frequentemente explorada por algoritmos de CS. Adotar métricas `p com menores valores de p, apesar de recair em problemas não-convexos, pode possibilitar uma redução ainda maior de medidas. Imagens são sinais de grande dimensão. Por esta razão, técnicas de reconstrução que se baseiam em CS recorrem a métodos indiretos para a realização de operações matriciais, já que o armazenamento das matrizes que modelam o problema é inviável durante a execução dos algoritmos. A estabilidade e a convergência dos métodos indiretos são afetadas pela redução do valor de p de modo que esta estratégia não pode ser bem explorada ao executar as operações matriciais indiretamente. Neste contexto, a presente pesquisa desenvolve a Estrutura de Reconstrução Direta (DRS) para formação de imagens médicas por meio da composição de sinais de menor dimensão, que são obtidos através de minimização de `p. Inicialmente, apresentamos o formalismo matemático para implementações genéricas dessa estrutura, em que não se assume nenhuma operação específica para a composição. Em um segundo momento, derivamos o modelo matemático e o problema de minimização para uma formulação que compõe a imagem a partir de sinais unidimensionais, que contém a informação de uma linha de medidas no plano de frequências. Implementamos esta formulação específica do DRS usando o IRLS (Iteratively Reweighted Least Squares) como algoritmo de minimização e a pré-filtragem para a representação esparsa. Realizamos quatro experimentos numéricos com o objetivo de investigar o comportamento dos algoritmos de CS ao reduzirmos o valor de p e avaliar a performance do DRS em comparação às técnicas que usam método indireto. Em nossos testes usamos tanto sinais artificiais como dados de imagens reais. Os resultados apontam que o DRS reconstrói satisfatoriamente as imagens médicas em condições favoráveis de esparsidade. A pré-filtragem não obteve a mesma eficiência em esparsificar os sinais reconstruídos pelo DRS em comparação ao que é verificado no caso dos algoritmos que usam método indireto.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).With the support of medical imaging technologies, healthcare workers are provided with relevant information about a patient’s condition when planning and following up on treatment. X-ray Computed Tomography (CT) and Magnetic Resonance (MR) are two of the most consolidated technologies in the field. These techniques yield anatomical images of specific planes or volumes. Although CT and MR exploit different physical principles, both collect measurements that can be modeled as the Fourier Transform coefficients of the image to be reconstructed. The reconstruction procedure refers to the stage of computing the desired image from the measurements acquired by the medical equipment. The acquisition usually requires the patient to stay in the same position for long periods, and, in the case of CT, there is the emission of ionizing radiation. Thus, such procedures should take place as safely and quickly as possible. A possible approach to address this issue is the development of reconstruction algorithms that can generate meaningful images for clinical practice from a reduced amount of measurements. Concepts of Compressive Sensing (CS) have been adopted in the devising of new algorithms for medical imaging to achieve a more efficient acquisition. This area of knowledge studies the reconstruction of signals from incomplete measurements by solving underdetermined linear systems. The signal of interest is the solution whose most of the coefficients are null. That is, the reconstructed signal is assumed to have a sparse representation in a known domain. Minimizing `p (0 < p ≤ 1) is a strategy often exploited by CS algorithms. Adopting `p metrics with smaller values of p, even leading to non-convex problems, opens up the possibility of further reductions in the number of measurements. Images are large signals. For this reason, CS-based reconstruction techniques rely on indirect methods to perform matrix operations because the storage of the matrices that model the problem is impractical during the execution of the algorithms. The stability and convergence of indirect methods are affected by reducing the value of p so that this strategy cannot be well exploited when performing matrix operations indirectly. In this background, the present research devises the Direct Reconstruction Structure (DRS) for medical image formation through the composition of lower-dimensional signals, which are obtained through `p minimization. First, we present the mathematical formalism for generic implementations of this structure, which makes no assumptions about the operation for composition. Following, we derive the mathematical model and the minimization problem for a formulation that composes the image from onedimensional signals, which contain the information of a row of measurements in the frequency plane. We implemented that specific DRS formulation using the Iteratively Reweighted Least Squares (IRLS) as the minimization algorithm and prefiltering for sparse representation. We conducted four numerical experiments to investigate the behavior of the CS algorithms when reducing the value of p and evaluate the performance of DRS compared to techniques using an indirect method. In our tests, we used both artificial signals and actual image data. The results suggest that DRS can satisfactorily reconstruct medical images in good sparsity conditions. Prefiltering did not achieve the same effect in sparsifying the signals reconstructed by DRS compared to the case of algorithms using the indirect method

Advanced Restoration Techniques for Images and Disparity Maps

With increasing popularity of digital cameras, the field of Computa- tional Photography emerges as one of the most demanding areas of research. In this thesis we study and develop novel priors and op- timization techniques to solve inverse problems, including disparity estimation and image restoration. The disparity map estimation method proposed in this thesis incor- porates multiple frames of a stereo video sequence to ensure temporal coherency. To enforce smoothness, we use spatio-temporal connec- tions between the pixels of the disparity map to constrain our solution. Apart from smoothness, we enforce a consistency constraint for the disparity assignments by using connections between the left and right views. These constraints are then formulated in a graphical model, which we solve using mean-field approximation. We use a filter-based mean-field optimization that perform efficiently by updating the dis- parity variables in parallel. The parallel updates scheme, however, is not guaranteed to converge to a stationary point. To compare and demonstrate the effectiveness of our approach, we developed a new optimization technique that uses sequential updates, which runs ef- ficiently and guarantees convergence. Our empirical results indicate that with proper initialization, we can employ the parallel update scheme and efficiently optimize our disparity maps without loss of quality. Our method ranks amongst the state of the art in common benchmarks, and significantly reduces the temporal flickering artifacts in the disparity maps. In the second part of this thesis, we address several image restora- tion problems such as image deblurring, demosaicing and super- resolution. We propose to use denoising autoencoders to learn an approximation of the true natural image distribution. We parametrize our denoisers using deep neural networks and show that they learn the gradient of the smoothed density of natural images. Based on this analysis, we propose a restoration technique that moves the so- lution towards the local extrema of this distribution by minimizing the difference between the input and output of our denoiser. Weii demonstrate the effectiveness of our approach using a single trained neural network in several restoration tasks such as deblurring and super-resolution. In a more general framework, we define a new Bayes formulation for the restoration problem, which leads to a more efficient and robust estimator. The proposed framework achieves state of the art performance in various restoration tasks such as deblurring and demosaicing, and also for more challenging tasks such as noise- and kernel-blind image deblurring. Keywords. disparity map estimation, stereo matching, mean-field optimization, graphical models, image processing, linear inverse prob- lems, image restoration, image deblurring, image denoising, single image super-resolution, image demosaicing, deep neural networks, denoising autoencoder