This project demonstrates how linear regression combined with Fourier features can be used to compress images efficiently. Instead of working directly with pixel values, the data is transformed into a set of sine and cosine features based on Fourier series, allowing for effective compression with reduced storage requirements.

• A basic linear regression model is trained on new Fourier-transformed data.
• Tested across grayscale and colored images with CIFAR-10 dataset.
• Uses Scikit's LinearRegression with default settings

• The sine-cosine form of Fourier series is used to replace raw pixel values with frequency-based features.
• Each sample corresponds to a specific frequency of the wave, and a linear regression model learns the amplitudes of these frequencies.
• Fourier series equation (sine-cosine form)

• Compression Achieved: Compression resulted in smaller image sizes than the original data without significant loss of clarity.
• Visualization of Clarity:
  • Plotted the compressed and original versions to observe how quality improves with increasing Fourier samples.
  • Beyond a certain threshold, increasing samples no longer improved clarity.

• Computational Complexity:
  • The approach scales with $O(N^2)$, where $N$ is the number of pixels, making it impractical for large images.
  • FFT (Fast Fourier Transform) offers a faster $O(N log N)$ alternative for large datasets.
• Hyperparameter Tuning: The number of Fourier samples and period were chosen manually without extensive tuning.
• Not Suitable for Bigger Images: Large images would require advanced models like neural networks for better performance.

• Hyperparameter Tuning: Experiment with different sample sizes and periods to optimize for accuracy vs. compression ratio.
• Use Autoencoders: Investigate the use of autoencoders for frequency-based feature extraction and compression.

• Wikipedia for the Fourier series equations.
• CIFAR-10 Dataset for sample images used during testing.