Signal Recovery Using a Spiked Mixture Model

TL;DR

This paper introduces the spiked mixture model (SMM) and an EM algorithm for signal recovery, demonstrating superior performance over traditional models in low SNR regimes across biomedical and computer vision applications.

Contribution

The paper presents the novel SMM and an EM algorithm for effective signal recovery, outperforming Gaussian mixture models in challenging noisy environments.

Findings

SMM outperforms GMM in low SNR regimes

SMM successfully applied to biomedical imaging data

SMM effectively segments hyperspectral images

Abstract

We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all parameters of the SMM. Numerical experiments show that in low signal-to-noise ratio regimes, and for data types where the SMM is relevant, SMM surpasses the more traditional Gaussian mixture model (GMM) in terms of signal recovery performance. The broad relevance of the SMM and its corresponding EM recovery algorithm is demonstrated by applying the technique to different data types. The first case study is a biomedical research application, utilizing an imaging mass spectrometry dataset to explore the molecular content of a rat brain tissue section at micrometer scale. The second case study demonstrates SMM performance in a computer vision application, segmenting a hyperspectral imaging dataset into underlying patterns. While the measurement modalities differ substantially, in both case studies SMM is shown to recover signals that were missed by traditional methods such as k-means clustering and GMM.