Unsupervised Segmentation of Random Discrete Data Hidden With Switching Noise Distributions

TLDR

Hidden Markov models are robust but struggle with nonstationary data, whereas triplet Markov models address this limitation with richer formalism while maintaining linear computational complexity. This letter proposes a new triplet Markov chain that enables unsupervised restoration of random discrete data corrupted by switching noise distributions. The authors present parameter‑estimation and MPM restoration algorithms for the proposed model. Experiments on synthetic data and real images demonstrate that the new model outperforms the standard hidden Markov chain.

Abstract

Hidden Markov models are very robust and have been widely used in a wide range of application fields; however, they can prove some limitations for data restoration under some complex situations. These latter include cases when the data to be recovered are nonstationary. The recent triplet Markov models have overcome such difficulty thanks to their rich formalism, that allows considering more complex data structures while keeping the computational complexity of the different algorithms linear to the data size. In this letter, we propose a new triplet Markov chain that allows the unsupervised restoration of random discrete data hidden with switching noise distributions. We also provide genuine parameters estimation and MPM restoration algorithms. The new model is validated through experiments conducted on synthetic data and on real images, whose results show its interest with respect to the standard hidden Markov chain.