An unsupervised algorithm for hybrid/morphological signal decomposition

The main contribution presented here is an adaptive/unsupervised iterative thresholding algorithm for sparse representation of signals which can be modeled as the sum of two components. Such Hybrid or Morphological representations are known to be well adapted for applications in image or audio signal processing. The proposed algorithm uses a Bernoulli-Gaussian prior on the synthesis coefficients of the signal, with morphological depending parameters. Using an EM-framework introduced by Figueiredo and Nowak in the case of the convex ℓ₁ prior, we derive an unsupervised algorithm in the spirit of ISTA, with iteratively adapted thresholding/shrinkage.