Iterative hard thresholding for compressed sensing
Iterative hard thresholding for compressed sensing
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DOI：
10.1016/j.acha.2009.04.002
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发表时间：
2009-11-01
影响因子：
2.5
通讯作者：
Davies, Mike E.
中科院分区：
文献类型：
--
作者：
Blumensath, Thomas;Davies, Mike E.
压缩感知是一种对低于奈奎斯特速率的可压缩信号进行采样的技术，同时仍然允许对信号进行接近最佳的重构。在本文中，我们提出了一个理论分析的迭代硬阈值算法时，适用于压缩感知恢复问题。我们证明了该算法具有以下性质（在论文的正文中做得更精确）它给出了近-最优误差保证。它对观测噪声具有鲁棒性。它成功地使用了最少数量的观测。它可以与任何可以计算算子及其伴随的采样算子一起使用。内存需求与问题大小呈线性关系。它的每次迭代计算复杂度与测量算子或其伴随算子的应用。它只需要固定的迭代次数，这只取决于信号信噪比的对数。它的性能保证是一致的，因为它们只取决于采样算子和信号稀疏性的性质。(C)2009 Elsevier Inc. All rights reserved.
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. in this paper we present a theoretical analysis of the iterative hard thresholding algorithm when applied to the compressed sensing recovery problem. We show that the algorithm has the following properties (made more precise in the main text of the paper)It gives near-optimal error guarantees.It is robust to observation noise.It succeeds with a minimum number of observations.It can be used with any sampling operator for which the operator and its adjoint can be computed.The memory requirement is linear in the problem size.Its computational complexity per iteration is of the same order as the application of the measurement operator or its adjoint.It requires a fixed number of iterations depending only on the logarithm of a form of signal to noise ratio of the signal.Its performance guarantees are uniform in that they only depend on properties of the sampling operator and signal sparsity. (C) 2009 Elsevier Inc. All rights reserved.