Sparse Signal Reconstruction via ECME Hard Thresholding
Sparse Signal Reconstruction via ECME Hard Thresholding
复制标题
通过 ECME 硬阈值重建稀疏信号
DOI：
10.1109/tsp.2012.2203818
复制
发表时间：
2012
影响因子：
5.4
通讯作者：
Dogandzic, Aleksandar
中科院分区：
文献类型：
--
作者：
Qiu, Kun;Dogandzic, Aleksandar
我们提出了一个稀疏信号重建的概率模型，并开发了几种新的算法来计算最大似然（ML）参数估计在这个模型下。测量遵循欠定线性模型，其中回归系数向量是未知确定性稀疏信号分量和具有未知方差的零均值白色高斯分量的和。我们的重建方案是基于期望条件最大化（ECME）迭代，其目的是最大化的似然函数相对于未知的参数为一个给定的信号稀疏水平。与现有的迭代硬阈值（IHT）方法相比，ECME算法包含一个额外的乘法项，并保证单调收敛的广泛的传感（回归）矩阵。我们提出了一个双超松弛（DORE）阈值方案，用于加速ECME迭代。我们证明，在一定的温和条件下，ECME和DORE迭代收敛到局部极大值的似然函数。ECME和DORE迭代可以在小规模应用中精确地实现，并且对于使用正交行的重要类别的大规模感测算子，例如，部分快速傅立叶变换（FFT）。如果信号的稀疏性水平是未知的，我们引入了一个无约束的稀疏性选择（USS）的标准和调谐免费的自动双超松弛（ADORE）阈值的方法，采用USS估计的稀疏性水平。我们通过使用模拟和真实的X射线CT数据的一维模拟和二维图像重建实验来比较提出的和现有的稀疏信号重建方法。
We propose a probabilistic model for sparse signal reconstruction and develop several novel algorithms for computing the maximum likelihood (ML) parameter estimates under this model. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown deterministic sparse signal component and a zero-mean white Gaussian component with an unknown variance. Our reconstruction schemes are based on an expectation-conditional maximization either (ECME) iteration that aims at maximizing the likelihood function with respect to the unknown parameters for a given signal sparsity level. Compared with the existing iterative hard thresholding (IHT) method, the ECME algorithm contains an additional multiplicative term and guarantees monotonic convergence for a wide range of sensing (regression) matrices. We propose a double overrelaxation (DORE) thresholding scheme for accelerating the ECME iteration. We prove that, under certain mild conditions, the ECME and DORE iterations converge to local maxima of the likelihood function. The ECME and DORE iterations can be implemented exactly in small-scale applications and for the important class of large-scale sensing operators with orthonormal rows used e.g., partial fast Fourier transform (FFT). If the signal sparsity level is unknown, we introduce an unconstrained sparsity selection (USS) criterion and a tuning-free automatic double overrelaxation (ADORE) thresholding method that employs USS to estimate the sparsity level. We compare the proposed and existing sparse signal reconstruction methods via one-dimensional simulation and two-dimensional image reconstruction experiments using simulated and real X-ray CT data.