Goal: comparison with Xavier’s implementation of primal-dual, audio pre-processing.
Related notebooks: comparison_xavier, gtzan, audio_preprocessing.
- Prototype on images:
- Dictionary is indeed full. The constraint less or equal instead of less is however more efficient as it is convex.
- Comparison with Xavier’s implementation and dataset (each patch has a zero mean, one patch per pixel).
- Obtained dictionary is very similar despite very different implementations (algorithms and platform).
- My implementation is slower because of numpy’s implementation of BLAS operations. We will switch to ATLAS or OpenBLAS.
- My Z is sparser despite a larger \(\|Z\|_1\) objective.
- Why using an under-complete dictionary, i.e. \(m < n\) ? For speed only.
- More iterations give a better convergence, i.e. sharper atoms.
- Improvements of the description of the optimization schemes and the graph definition.
- Implementation of the audio pre-processing steps: frames and CQT. See the audio_preprocessing notebook for details.
- Convert the GTZAN dataset to an HDF5 store. Load and save all subsequent data in HDF5. See the gtzan notebook for details.
- Many improvements to the PyUNLocBoX. See the repository for details.
- LCN can be viewed as one step of inverting the heat equation. Similar to shock filters .
 Osher, S., & Rudin, L. I. (1990). Feature-oriented image enhancement using shock filters. SIAM Journal on Numerical Analysis, 27(4), 919-940.