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Image Completion with QuatIca

Overview

QuatIca provides powerful quaternion-based image completion capabilities using advanced matrix decomposition techniques. This application demonstrates how quaternion matrices can effectively restore missing or corrupted image data.

Key Features

  • Multiple completion strategies for different image types and corruption patterns
  • Real image completion for practical restoration scenarios
  • Synthetic image completion for controlled testing and validation
  • Small image completion for rapid prototyping and development

Available Scripts

Real Image Completion

python applications/image_completion/script_real_image_completion.py
Handles real-world image completion tasks with various corruption patterns and noise levels.

Synthetic Image Completion

python applications/image_completion/script_synthetic_image_completion.py
Generates synthetic test cases for systematic evaluation of completion algorithms.

Small Image Completion

python applications/image_completion/script_small_image_completion.py
Optimized for quick testing with smaller image dimensions.

Methodology

The image completion process leverages quaternion matrix factorization:

  1. Quaternion Encoding: Images are represented as quaternion matrices where each quaternion encodes color channel information
  2. Matrix Decomposition: Advanced quaternion SVD and factorization techniques identify underlying structure
  3. Completion Algorithm: Missing pixels are estimated using low-rank quaternion matrix completion
  4. Iterative Refinement: Newton-Schulz and other iterative methods refine the completion

Applications

  • Photo restoration - Repair damaged or corrupted images
  • Missing data recovery - Complete images with systematic missing regions
  • Noise reduction - Clean corrupted image data while preserving structure
  • Compression artifacts removal - Restore quality in heavily compressed images

Performance Benefits

QuatIca's quaternion-based approach offers several advantages: - Color coherence - Naturally preserves color relationships across channels - Structural preservation - Maintains geometric features and patterns - Computational efficiency - Optimized quaternion operations reduce processing time - Robust completion - Handles various corruption patterns effectively

Getting Started

  1. Prepare your image in a supported format (PNG, JPEG)
  2. Choose the appropriate script based on your completion task
  3. Configure parameters for corruption type and completion method
  4. Run the completion and examine results in output_figures/

For detailed parameter descriptions and advanced usage, see the individual script documentation.