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Updated: Jun 15, 2026
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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
Published on: December 3, 2013
Demosaicking by alternating projections: theory and fast one-step implementation
Yue M Lu1, Mina Karzand, Martin Vetterli
1Audiovisual Communications Laboratory, School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne, Switzerland. yuelu@seas.harvard.edu
Summary
This study analyzes the alternating projections (AP) color image demosaicking algorithm. We demonstrate its optimality and introduce a novel one-step method for significant computational savings.
Area of Science:
- Digital Imaging
- Computer Vision
- Image Processing
Background:
- Color image demosaicking is crucial for digital imaging pipelines.
- The alternating projections (AP) algorithm is a widely cited demosaicking method.
- A key limitation of the AP algorithm is its high computational complexity.
Purpose of the Study:
- To rigorously analyze the convergence properties of the AP demosaicking algorithm.
- To establish the optimality of the AP algorithm by linking it to a constrained quadratic minimization problem.
- To develop a computationally efficient, single-step implementation of the AP algorithm.
Main Methods:
- Convergence analysis of the AP algorithm, demonstrating it as a contraction mapping.
- Mathematical formulation showing the fixed point as a solution to a constrained quadratic minimization problem.
- Application of polyphase representation for a single-step, linear filtering implementation.
Main Results:
- The AP algorithm converges to a unique fixed point, proving its convergence property.
- The fixed point is the optimal solution to a specific constrained quadratic minimization problem.
- A novel one-step method using polyphase filtering achieves results comparable to the original AP algorithm.
Conclusions:
- The AP algorithm is mathematically optimal for color image demosaicking.
- The proposed one-step polyphase domain implementation offers substantial computational savings (approximately one order of magnitude).
- This research enhances the efficiency and understanding of a fundamental image processing algorithm.
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