Signal stochastic decomposition over continuous dictionaries

Zacharie Naulet (1) , Eric Barat (1)

1 LM2S - Laboratoire Modélisation et Simulation de Systèmes

We propose a Bayesian nonparametrics method, including algorithm for posterior computation, for the sparse regression problem. Our method applies in a general setting, when there are direct or indirect noisy observations of the signal. We try to make a wide focus on smoothness properties and sparsity of the approximate. As an example, we consider the ill-posed inverse problem of Quantum Homodyne Tomography.

Keywords: Algorithms; Artificial intelligence; Computation theory; Inverse problems; Learning systems; Light sources; Stochastic models; Stochastic systems; Sparse regression; Stochastic decomposition; Noisy observations; ILL-posed inverse problem; Signal processing; Quantum homodyne tomography; Coorbit Theory; Bayesian nonparametrics

Domains: Computer Science [cs]; Signal and Image Processing; Computer Science [cs]; Numerical Analysis [cs.NA]; Life Sciences [q-bio]; Bioengineering; Statistics [stat]; Methodology [stat.ME]

Zacharie Naulet, Eric Barat. Signal stochastic decomposition over continuous dictionaries. 2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), Sep 2014, Reims, France. pp.6958857, ⟨10.1109/MLSP.2014.6958857⟩. ⟨cea-01830639⟩