First-order Convex Optimization Methods for Signal and Image Processing

Research output: Book/ReportPh.D. thesisResearch

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Abstract

In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple-description problem. We finally present the contributions of the thesis.

The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third papers concern discrete linear inverse problems and reliable numerical reconstruction software. The last two papers present a convex optimization formulation of the multiple-description problem and a method to solve it in the case of large-scale instances.
Original languageEnglish
Place of PublicationAalborg
Volume1
Number of pages182
ISBN (Print)978-87-92328-76-2
Publication statusPublished - 15 Feb 2012

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Convex optimization
Signal processing
Image processing
Inverse problems
Gradient methods
Lagrange multipliers

Keywords

  • Convex optimisation
  • Signal Processing
  • image processing
  • Inverse modeling

Cite this

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title = "First-order Convex Optimization Methods for Signal and Image Processing",
abstract = "In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple-description problem. We finally present the contributions of the thesis.The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third papers concern discrete linear inverse problems and reliable numerical reconstruction software. The last two papers present a convex optimization formulation of the multiple-description problem and a method to solve it in the case of large-scale instances.",
keywords = "Convex optimisation, Signal Processing, image processing, Inverse modeling",
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First-order Convex Optimization Methods for Signal and Image Processing. / Jensen, Tobias Lindstrøm.

Aalborg, 2012. 182 p.

Research output: Book/ReportPh.D. thesisResearch

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N2 - In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple-description problem. We finally present the contributions of the thesis.The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third papers concern discrete linear inverse problems and reliable numerical reconstruction software. The last two papers present a convex optimization formulation of the multiple-description problem and a method to solve it in the case of large-scale instances.

AB - In this thesis we investigate the use of first-order convex optimization methods applied to problems in signal and image processing. First we make a general introduction to convex optimization, first-order methods and their iteration complexity. Then we look at different techniques, which can be used with first-order methods such as smoothing, Lagrange multipliers and proximal gradient methods. We continue by presenting different applications of convex optimization and notable convex formulations with an emphasis on inverse problems and sparse signal processing. We also describe the multiple-description problem. We finally present the contributions of the thesis.The remaining parts of the thesis consist of five research papers. The first paper addresses non-smooth first-order convex optimization and the trade-off between accuracy and smoothness of the approximating smooth function. The second and third papers concern discrete linear inverse problems and reliable numerical reconstruction software. The last two papers present a convex optimization formulation of the multiple-description problem and a method to solve it in the case of large-scale instances.

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BT - First-order Convex Optimization Methods for Signal and Image Processing

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