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Dyadic Partition-Based Training Schemes for TV/TGV Denoising.

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Summary
This summary is machine-generated.

This study introduces a new method for automatic image denoising parameter tuning using multilevel approaches. It optimizes space-dependent parameters on dyadic grids, improving performance over constant parameters.

Keywords:
Bilevel optimizationBox constraintDiscontinuous weightsSpatially-dependent regularization parametersTotal generalized variationTotal variation

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Area of Science:

  • Image processing and computer vision
  • Mathematical optimization
  • Applied mathematics

Background:

  • Total Variation (TV) and Total Generalized Variation (TGV) are effective image denoising methods but require careful parameter tuning.
  • Variational models for image denoising often depend critically on parameter selection, impacting performance.
  • Automatic parameter selection methods, such as multilevel approaches, are needed to overcome this limitation.

Purpose of the Study:

  • To develop and analyze a multilevel approach for automatic image denoising parameter selection.
  • To investigate space-dependent parameters that are piecewise constant on dyadic grids, with the grid structure as part of the optimization.
  • To prove the existence of minimizers and optimal partitions for these space-dependent parameters.

Main Methods:

  • Proving the existence of minimizers for fixed discontinuous parameters under mild data assumptions.
  • Establishing the equivalence of these assumptions to standard box constraints on parameters.
  • Developing a subdivision scheme for optimal partitions integrated with bilevel optimization for scalar parameters.

Main Results:

  • Existence of minimizers and finite optimal partitions for space-dependent parameters is proven.
  • The proposed method demonstrates improved denoising performance on test images compared to methods using constant optimized parameters.
  • The numerical scheme effectively optimizes piecewise constant, space-dependent parameters on dyadic grids.

Conclusions:

  • Automatic tuning of space-dependent parameters in TV and TGV image denoising is feasible and effective.
  • The developed multilevel approach with dyadic grids offers a robust solution for parameter selection in image denoising.
  • This work advances variational methods in image processing by providing a more adaptive and performant parameter optimization strategy.