Compressive Sensing by Learning a Gaussian Mixture Model From Measurements
Compressive Sensing by Learning a Gaussian Mixture Model From Measurements
复制标题
DOI：
10.1109/tip.2014.2365720
复制
发表时间：
2015-01
影响因子：
10.6
通讯作者：
Jianbo Yang;X. Liao;Xin Yuan;P. Llull;D. Brady;G. Sapiro;L. Carin
中科院分区：
文献类型：
--
作者：
Jianbo Yang;X. Liao;Xin Yuan;P. Llull;D. Brady;G. Sapiro;L. Carin
从高斯混合模型（GMM）中提取的信号的压缩感知允许从不完全线性测量中进行封闭形式的最小均方误差重构。由于很难获得与被测信号统计量相匹配的训练信号，因此通常无法先验地获得精确的GMM信号模型。我们建议通过直接基于信号的压缩测量就地学习信号模型来解决这个问题，而不需要借助其他信号来训练模型。我们方法的一个关键特征是，被感知的信号被视为随机变量，并在似然中进行积分。我们推导了一个最大边际似然估计器（MMLE），它最大化底层信号的GMM的似然，只给出它们的线性压缩测量。我们将MMLE扩展为以低秩协方差矩阵为主的GMM，以提高计算速度。我们报告了大量的实验结果，包括图像绘制、高速视频的压缩感知和压缩高光谱成像（后两者基于真实的压缩相机）。结果表明，所提出的方法优于国家的最先进的方法显著差额。
Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.