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New ℓ2 - ℓ0 algorithm for single-molecule localization microscopy.

Arne Bechensteen1, Laure Blanc-Féraud1, Gilles Aubert2

  • 1Université Côte d'Azur, CNRS, INRIA, Laboratoire I3S,UMR 7271,06903 Sophia Antipolis, France.

Biomedical Optics Express
|March 6, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces novel biconvex algorithms (CoBic and PeBic) for precise single-molecule localization microscopy. These methods improve fluorophore identification in dense, noisy images, advancing super-resolution microscopy techniques.

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Area of Science:

  • Biophysics
  • Optical Microscopy
  • Computational Imaging

Background:

  • Single-molecule localization microscopy (SMLM) is crucial for super-resolution imaging.
  • Accurate fluorophore localization is challenging due to image noise and high emitter density.
  • Existing methods struggle with precise localization in complex SMLM datasets.

Purpose of the Study:

  • To develop advanced algorithms for accurate fluorophore localization in SMLM.
  • To address the challenge of localizing emitters in blurred, noisy, and high-density acquisitions.
  • To reformulate and solve the ℓ2-ℓ0 minimization problem for SMLM.

Main Methods:

  • Focus on a grid-based approach using ℓ2 least-squares and ℓ0 pseudo-norm sparsity.
  • Formulate the ℓ0 pseudo-norm as a convex minimization problem using an auxiliary variable.
  • Propose an exact biconvex reformulation for constrained and penalized ℓ2-ℓ0 problems.
  • Develop and apply Constrained Biconvex (CoBic) and Penalized Biconvex (PeBic) minimization algorithms.

Main Results:

  • Successfully applied CoBic and PeBic algorithms to SMLM data.
  • Demonstrated improved fluorophore localization accuracy compared to existing methods.
  • Validated the effectiveness of the biconvex reformulation for ℓ2-ℓ0 optimization.

Conclusions:

  • The proposed CoBic and PeBic algorithms offer a robust solution for SMLM fluorophore localization.
  • Biconvex optimization provides an effective framework for handling ℓ2-ℓ0 minimization in SMLM.
  • These advancements enhance the capabilities of super-resolution microscopy for biological imaging.