用新模型从噪声中恢复微弱信号，比传统方法更准。
Signal Recovery Using a Spiked Mixture Model
- 提出带尖峰的混合模型，用新EM算法同时估计信号和噪声参数。
- 在低信噪比下，对生物成像和高光谱图像数据恢复效果优于GMM。
- 适用于复杂噪声场景，适合做信号提取的科研与工程人员参考。
我们提出尖峰混合模型（SMM），用于从大量随机缩放且含噪声的观测中估计一组信号。随后设计了一种新型期望最大化（EM）算法以恢复SMM的所有参数。数值实验表明，在低信噪比条件下，且在SMM适用的数据类型中，SMM在信号恢复性能上优于传统的高斯混合模型（GMM）。通过应用于不同类型数据，展示了SMM及其对应EM算法的广泛适用性。第一项案例研究是生物医学应用，使用质谱成像数据集，在微米尺度分析大鼠脑组织的分子组成；第二项案例研究展示其在计算机视觉中的表现，将高光谱影像数据分割为潜在模式。尽管测量模态差异显著，两项研究均表明SMM能恢复传统方法（如k-means聚类和GMM）遗漏的信号。
原文摘要 · Abstract (English)
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.
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