Signal Recovery Using a Spiked Mixture Model
Journal:
arXiv
Published Date:
Jan 3, 2025
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.
