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A linearly convergent first-order algorithm for total variation minimisation in image processing.

Cong D Dang1, Kaiyu Dai2, Guanghui Lan1

  • 1Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA.

International Journal of Bioinformatics Research and Applications
|January 23, 2014
PubMed
Summary
This summary is machine-generated.

This study presents a novel formulation for total variation minimization in image denoising. A new first-order method achieves linear convergence with nearly dimension-independent iteration complexity for this problem.

Keywords:
complexityfirst–order methodsimage denoisingimage processinglinear rate of convergencereformulationtotal variation

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Area of Science:

  • Image processing and computer vision
  • Numerical analysis and optimization

Background:

  • Image denoising is crucial for enhancing image quality.
  • Total variation minimization is a common technique for image denoising.
  • Existing methods may face challenges with convergence and computational complexity.

Purpose of the Study:

  • To introduce a new formulation for total variation minimization in image denoising.
  • To develop an efficient first-order method for solving the reformulated problem.
  • To analyze the convergence properties and iteration complexity of the proposed method.

Main Methods:

  • A novel mathematical formulation for total variation minimization is proposed.
  • A linearly convergent first-order optimization method is developed.
  • Theoretical analysis is conducted to determine iteration complexity bounds.

Main Results:

  • The new formulation effectively addresses image denoising.
  • The proposed first-order method demonstrates linear convergence.
  • A nearly dimension-independent iteration complexity bound is established.

Conclusions:

  • The introduced formulation and method offer an efficient approach to image denoising.
  • The theoretical findings suggest scalability and robustness for various image sizes.
  • This work advances the field of image restoration and optimization techniques.