Meeting 7 (17.04)

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 [1].


[1] Osher, S., & Rudin, L. I. (1990). Feature-oriented image enhancement using shock filters. SIAM Journal on Numerical Analysis, 27(4), 919-940.

Michaël Defferrard

I am currently pursuing master studies in Information Technologies at EPFL. My master project, conducted at the LTS2 Signal Processing laboratory led by Prof. Pierre Vandergheynst, is about audio classification with structured deep learning. I previously devised an image inpainting algorithm. It used a non-local patch graph representation of the image and a structure detector which leverages the graph representation and influences the fill-order of the exemplar-based algorithm. I've been a Research Assistant in the lab, where I did investigate Super Resolution methods for Mass Spectrometry. I develop PyUNLocBoX, a convex optimization toolbox in Python.

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