Predictive Coding for Image Compression

This project implements predictive coding algorithms for image compression, comparing lossless and lossy approaches. The implementation processes an X-ray image and evaluates the compression performance using Signal-to-Noise Ratio (SNR) metrics.

Overview

Predictive coding is a technique used in image compression that predicts pixel values based on neighboring pixels and encodes only the prediction error (residual). This approach exploits spatial redundancy in images to achieve compression.

Features

• Lossless Predictive Coding: Preserves all image information by encoding exact prediction errors
• Lossy Predictive Coding: Uses quantization to reduce data size while maintaining acceptable image quality
• SNR Analysis: Compares the performance of both methods using Signal-to-Noise Ratio calculations

Algorithm Details

Lossless Predictive Coding

• Uses a simple predictor: predicted_value = (pixel_right + pixel_below) / 2
• Encodes the exact prediction error: error = actual_value - predicted_value
• No information loss - perfect reconstruction possible

Lossy Predictive Coding

• Uses an adaptive predictor that chooses between:
  • Horizontal prediction: predicted_value = pixel_left
  • Vertical prediction: predicted_value = pixel_above
• Selection is based on which direction has smaller gradient
• Quantizes the prediction error using a 6-level quantizer:
  • Error ranges: [-∞, -40/255], [-40/255, -10/255], [-10/255, 0], [0, 10/255], [10/255, 40/255], [40/255, +∞]
  • Quantized values: -64/255, -16/255, -4/255, 4/255, 16/255, 64/255

Requirements

• Python 3.x
• NumPy
• Matplotlib

Installation

pip install numpy matplotlib

Usage

1. Ensure x-ray.png is in the same directory as the notebook
2. Open PredictiveCoding.ipynb in Jupyter Notebook or JupyterLab
3. Run all cells sequentially

Output

The notebook generates several visualizations:

1. Original Image: Displays the input X-ray image and its histogram
2. Lossless Results: Shows the prediction image and error histogram
3. Lossy Results: Shows the quantized prediction image and error histogram
4. SNR Comparison: Prints Signal-to-Noise Ratio for both methods

Expected Results

• SNR Lossless: ~79.59 dB (higher is better, lossless has perfect reconstruction)
• SNR Lossy: ~65.73 dB (lower due to quantization, but still acceptable quality)

File Structure

ImageCoding_PredictiveCoding/
├── PredictiveCoding.ipynb    # Main notebook with implementation
├── x-ray.png                  # Input image
├── README.md                  # This file
└── LICENSE                    # License file

Notes

• The lossless method provides perfect reconstruction but requires storing all prediction errors
• The lossy method achieves better compression at the cost of some image quality
• SNR values may vary slightly depending on the input image characteristics

License

This project is licensed under the MIT License - see the LICENSE file for details.

References

Predictive coding is a fundamental technique in image compression, used in standards like JPEG-LS and as a component in more complex codecs.