The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple

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Abstract By assuming that images of interest can be sparsely modelled by some transform, the sparsity-based regularization has been one promising approach for solving many ill-posed inverse problems in image recovery. One often-used type of systems for sparsifying images is wavelet tight frames

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