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Surface Mapping of Earth-like Exoplanets using Single Point Light Curves
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Total variation projection with first order schemes.

Jalal M Fadili1, Gabriel Peyre

  • 1GREYC CNRS-ENSICAEN-Université de Caen, 14050 Caen Cedex, France. jalal.fadili@greyc.ensicaen.fr

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 30, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a novel algorithm for image projection with bounded total variation (TV). The method uses dual formulation and iterative soft thresholding, offering faster convergence for various image processing tasks.

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Area of Science:

  • Image processing
  • Optimization
  • Computer vision

Background:

  • Total variation (TV) minimization is crucial for image processing tasks.
  • Efficiently computing projections onto TV-constrained sets is challenging.

Purpose of the Study:

  • To develop a new, efficient algorithm for projecting images onto the set of functions with bounded total variation.
  • To analyze the convergence properties of the proposed algorithm.
  • To demonstrate the algorithm's utility in various image processing applications.

Main Methods:

  • A dual formulation of the projection problem is employed.
  • First-order non-smooth optimization methods are utilized.
  • Iterative soft thresholding is applied to the dual vector field.

Main Results:

  • A novel iterative projection algorithm is presented.
  • Convergence rates for the primal iterates are established.
  • The algorithm demonstrates competitive performance against state-of-the-art methods in terms of speed.

Conclusions:

  • The proposed TV projection algorithm is effective and efficient.
  • It serves as a valuable tool for inverse problems and texture synthesis.
  • Numerical results validate its applicability in denoising, inpainting, deconvolution, and tomography.