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Reconstruction of sparse signals from l1 dimensionality-reduced Cauchy random-projections
TLDR
This paper focuses on developing signal reconstruction algorithms from Cauchy random projections, where the large suite of reconstruction algorithms developed in compressive sensing perform poorly due to the lack of finite second-order statistics in the projections. Expand
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Alternate Direction Method of Multipliers for Unconstrained Structural Similarity-Based Optimization
TLDR
A new method based on the Alternate Direction Method of Multipliers (ADMM) for solving an unconstrained SSIM-based optimization problem. Expand
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Unconstrained Structural Similarity-Based Optimization
TLDR
We establish a general framework, along with a set of algorithms, for the incorporation of the Structural Similarity (SSIM) quality index measure as the fidelity, or “data fitting,” term in objective functions for optimization problems in image processing. Expand
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Function-valued Mappings and SSIM-based Optimization in Imaging
  • D. Otero
  • Computer Science, Mathematics
  • 27 August 2015
TLDR
In a few words, this thesis is concerned with two alternative approaches to imaging, namely, Function-valued Mappings (FVMs) and Structural Similarity Index Measure (SSIM)-based Optimization. Expand
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Reconstruction of Sparse Signals From $\ell_1$ Dimensionality-Reduced Cauchy Random Projections
TLDR
We proposed two algorithms to reconstruct a sparse signal from dimensionality reduced sketches in that are obtained using Cauchy random projections using explicit tail bounds for the geometric mean. Expand
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Solving Optimization Problems That Employ Structural Similarity As The Fidelity Measure
Many tasks in image processing are carried out by solving appropriate optimization problems. As is well known, the square of the Euclidian distance is widely used as a fitting term, even though itExpand
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A simple class of fractal transforms for hyperspectral images
TLDR
A complete metric space of function-valued mappings appropriate for the representation of hyperspectral images is introduced. Expand
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Generalized Restricted Isometry Property for alpha-stable random projections
  • D. Otero, G. Arce
  • Mathematics, Computer Science
  • IEEE International Conference on Acoustics…
  • 22 May 2011
TLDR
The Restricted Isometry Property (RIP) is an important concept in compressed sensing. Expand
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Structural Similarity-Based Optimization Problems with L^1 -Regularization: Smoothing Using Mollifiers
TLDR
In this paper we propose a new method of solving optimization problems involving the structural similarity image quality measure with \(L^1\)-regularization. Expand
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Hyperspectral Images as Function-Valued Mappings, Their Self-similarity and a Class of Fractal Transforms
TLDR
A formulation of hyperspectral images as function-valued mappings is introduced, along with a set of simple models of affine self-similarity for digital hyperspectrals. Expand
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