I am presenting an image denoising example that fully runs under my local scikits-learn fork. Coming soon near you!
The 400 square pixels area covering Lena’s face was distorted by additive gaussian noise with a standard deviation of 50 (pixel values are ranged 0-256.)
The dictionary contains 100 atoms of shape 4x4 and was trained using 10000 random patches extracted from the undistorted image. Then, each one of the four 100 square pixel areas was reconstructed using the dictionary learning model and a different transform method.
- OMP-1 reconstructs each patch as the closest dictionary atom, multiplied by a variable coefficient. This is similar to the idea of gain-shape vector quantization.
- OMP-2 is like OMP-1, but it considers 2 atoms instead of just one. This takes advantage of the fact that the natural dictionary atoms are of such nature to efficiently represent random image patches when combined.
- LARS finds a reconstruction of each image patch as a solution to a Lasso problem, solved using least angle regression.
- Thresholding is a simple and quick non-linearity that (as it is currently implemented, based on , where it is not intended for reconstruction but for classification) breaks the local brightness of the image fragment. The bottom right fragment was forcefully renormalized to stretch fit into the 0-256 range, but brightness differences can be seen.
[The importance of encoding versus training with sparse coding and vector quantization, Adam Coates and Andrew Y. Ng. In Proceedings of the Twenty-Eighth International Conference on Machine Learning, 2011.]: http://ai.stanford.edu/~ang/papers/icml11-EncodingVsTraining.pdf