Signal Recovery Using a Spiked Mixture Model

2025-01-03

AI Summary

Joint recovery of multiple signals under highly noisy, randomly scaled observations remains challenging due to the coupled sparsity and stochastic scaling inherent in real-world measurement processes. Method: This paper proposes the Spike Mixture Model (SMM), the first unified probabilistic framework that jointly characterizes both the sparse spike-like amplitude distribution of underlying signals and the randomness in observation scales. Leveraging this structural insight, we design a customized Expectation-Maximization (EM) algorithm tailored to SMM’s non-Gaussian, scale-heterogeneous likelihood—overcoming fundamental limitations of conventional Gaussian Mixture Models (GMMs) in low signal-to-noise ratio regimes. Contribution/Results: Evaluated on brain tissue mass spectrometry imaging and hyperspectral image segmentation, SMM significantly outperforms k-means and GMM, successfully reconstructing critical molecular distributions and spectral patterns previously missed by standard methods. These results demonstrate SMM’s superior capability to model realistic, complex observation mechanisms and achieve robust signal recovery under severe noise and scale uncertainty.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Signal Recovery
• Noisy Data
• Random Variations

Innovation

• Spike Mixture Model (SMM)
• EM Algorithm
• High Noise Signal Recovery