A Hamiltonian Monte Carlo method for non-smooth energy sampling

Lotfi Chaari*, Jean-Yves Tourneret, Caroline Chaux, Hadj Batatia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


Efficient sampling from high-dimensional distributions is a challenging issue that is encountered in many large data recovery problems. In this context, sampling using Hamiltonian dynamics is one of the recent techniques that have been proposed to exploit the target distribution geometry. Such schemes have clearly been shown to be efficient for multidimensional sampling but, rather, are adapted to distributions from the exponential family with smooth energy functions. In this paper, we address the problem of using Hamiltonian dynamics to sample from probability distributions having non-differentiable energy functions such as those based on the ℓ1 norm. Such distributions are being used intensively in sparse signal and image recovery applications. The technique studied in this paper uses a modified leapfrog transform involving a proximal step. The resulting nonsmooth Hamiltonian Monte Carlo method is tested and validated on a number of experiments. Results show its ability to accurately sample according to various multivariate target distributions. The proposed technique is illustrated on synthetic examples and is applied to an image denoising problem.

Original languageEnglish
Pages (from-to)5585-5594
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number21
Early online date27 Jun 2016
Publication statusPublished - 1 Nov 2016


  • Bayesian methods
  • Hamiltonian
  • leapfrog
  • MCMC
  • proximity operator
  • Sparse sampling

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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