Sparse Signal Reconstruction from Quantized Noisy Measurements via GEM Hard Thresholding
Sparse Signal Reconstruction from Quantized Noisy Measurements via GEM Hard Thresholding
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DOI：
10.1109/tsp.2012.2185231
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发表时间：
2012-05
影响因子：
5.4
通讯作者：
Kun Qiu;Aleksandar Dogandzic
中科院分区：
文献类型：
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作者：
Kun Qiu;Aleksandar Dogandzic
我们开发了一种从量化的嘈杂测量值中稀疏信号重建的广义期望最大化（GEM）算法。测量值遵循一个不确定的线性模型，其稀疏回归系数，由于添加剂白色高斯噪声而损坏，差异未知。这些测量值被量化为垃圾箱，仅用于重建垃圾箱指数。我们将非量化测量值视为缺失的数据，并提出了一种GEM迭代，旨在最大程度地提高相对于未知参数的可能性函数。在轻度条件下，我们的宝石迭代产生了单调的非偏变函数序列的收敛性，并且随着迭代次数的增长，两个连续的GEM信号之间的欧几里得距离为零。我们将所提出的方案与最新的凸松弛方法进行比较，以通过数值模拟进行量化压缩感测。
We develop a generalized expectation-maximization (GEM) algorithm for sparse signal reconstruction from quantized noisy measurements. The measurements follow an underdetermined linear model with sparse regression coefficients, corrupted by additive white Gaussian noise having unknown variance. These measurements are quantized into bins and only the bin indices are used for reconstruction. We treat the unquantized measurements as the missing data and propose a GEM iteration that aims at maximizing the likelihood function with respect to the unknown parameters. Under mild conditions, our GEM iteration yields a convergent monotonically nondecreasing likelihood function sequence and the Euclidean distance between two consecutive GEM signal iterates goes to zero as the number of iterations grows. We compare the proposed scheme with the state-of-the-art convex relaxation method for quantized compressed sensing via numerical simulations.