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Master's Dissertation
DOI
10.11606/D.45.2012.tde-02102012-162650
Document
Author
Full name
Boris Chullo Llave
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Birgin, Ernesto Julian Goldberg (President)
Bueno, Luis Felipe Cesar da Rocha
Hashimoto, Ronaldo Fumio
Title in Portuguese
Aplicação do método do Gradiente Espectral Projetado ao problema de Compressive Sensing
Keywords in Portuguese
Compressive Sensing
Gradiente Espectral Projetado.
Otimização Contínua
Processamento de Imagens
Abstract in Portuguese
A teoria de Compressive Sensing proporciona uma nova estratégia de aquisição e recuperação de dados com bons resultados na área de processamento de imagens. Esta teoria garante recuperar um sinal com alta probabilidade a partir de uma taxa reduzida de amostragem por debaixo do limite de Nyquist-Shanon. O problema de recuperar o sinal original a partir das amostras consiste em resolver um problema de otimização. O método de Gradiente Espectral Projetado é um método para minimizar funções suaves em conjuntos convexos que tem sido aplicado com frequência ao problema de recuperar o sinal original a partir do sinal amostrado. Este trabalho dedica-se ao estudo da aplicação do Método do Gradiente Espectral Projetado ao problema de Compressive Sensing.
Title in English
Applications of the Spectral Prjected Gradient for Compressive Sensing theory
Keywords in English
Compressive Sensing
Continuous Optimization
Image Processing
Spectral Projected Gradient.
Abstract in English
The theory of compressive sensing has provided a new acquisition strategy and data recovery with good results in the image processing area. This theory guarantees to recover a signal with high probability from a reduced sampling rate below the Nyquist-Shannon limit. The problem of recovering the original signal from the samples consists in solving an optimization problem. The Spectral Projected Gradient (SPG) is a method to minimize continuous functions over convex sets which often has been applied to the problem of recovering the original signal from sampled signals. This work is dedicated to the study and application of the Spectral Projected Gradient method to Compressive Sensing problems.
 
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bcllave.pdf (9.83 Mbytes)
Publishing Date
2012-10-18
 
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