Signal Recovery Using a Spiked Mixture Model
This addresses signal recovery problems in domains like biomedical imaging and computer vision, though it appears incremental as it builds on mixture models with specific adaptations.
The authors tackled the problem of estimating signals from noisy observations by introducing the spiked mixture model (SMM) and a novel EM algorithm, showing that SMM surpasses Gaussian mixture models in signal recovery performance, especially in low signal-to-noise ratio regimes.
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.