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Related Experiment Video

Updated: Jun 5, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Angular Synchronization by Eigenvectors and Semidefinite Programming.

A Singer1

  • 1Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544-1000 USA, amits@math.princeton.edu.

Applied and Computational Harmonic Analysis
|December 24, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient eigenvector method for angular synchronization, accurately estimating unknown angles from noisy offset measurements, even with a high percentage of outliers. The algorithm is fast and robust, succeeding with up to 90% outliers.

Related Experiment Videos

Last Updated: Jun 5, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Signal Processing
  • Optimization
  • Applied Mathematics

Background:

  • The angular synchronization problem involves estimating unknown angles from noisy offset measurements.
  • A key challenge is handling a large number of outlier measurements that provide no useful information.

Purpose of the Study:

  • To develop an efficient and robust algorithm for angle recovery in the presence of numerous outliers.
  • To analyze the performance of the proposed method using random matrix and information theory.

Main Methods:

  • An efficient recovery algorithm based on the top eigenvector of a specially designed Hermitian matrix.
  • Analysis using random matrix theory and information theory.
  • Exploration of connections to combinatorial optimization (Max-2-Lin mod L) and semidefinite relaxation.

Main Results:

  • The eigenvector method demonstrates extreme stability and succeeds with a high proportion of outliers (e.g., 90%).
  • Accurate estimation of 400 angles from over 196,000 measurements, with 90% outliers, in under a second.
  • Demonstrated extensions to other synchronization problems like time synchronization and surface reconstruction.

Conclusions:

  • The eigenvector method provides a highly effective solution for angular synchronization with significant outlier contamination.
  • The approach is computationally efficient and broadly applicable to related synchronization problems in various fields.