Fast methods for recovering sparse parameters in linear low rank models
Fast methods for recovering sparse parameters in linear low rank models
复制标题
线性低秩模型中恢复稀疏参数的快速方法
DOI：
10.1109/globalsip.2016.7906072
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
F. Marvasti
中科院分区：
文献类型：
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作者：
Ashkan Esmaeili;A. Amini;F. Marvasti
本文研究了从一组噪声线性组合中恢复稀疏权向量（参数向量）的问题。然而，只有关于表示线性组合的矩阵的部分信息是可用的。假设矩阵是一个低秩结构，一个自然的解决方案是首先对数据应用矩阵补全，然后解决由此产生的压缩感知问题。在海量MIMO和医疗数据等大数据应用中，矩阵补全步骤带来了巨大的计算负担。在这里，我们建议通过忽略稀疏向量中对应于零元素的列来减少补全任务的计算成本。为此，我们采用了一种技术来初始近似稀疏向量的支持度。我们进一步提出将部分矩阵补全和稀疏向量恢复统一为一个增广的四步问题。仿真结果表明，增强方法的性能最好，两种方法都优于自然两步法，计算量大大减少。
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion to the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.