Fast and Stable Signal Deconvolution via Compressible State-Space Models
Fast and Stable Signal Deconvolution via Compressible State-Space Models
复制标题
通过可压缩状态空间模型快速稳定的信号反卷积
DOI：
10.1101/092643
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
B. Babadi
中科院分区：
文献类型：
--
作者：
A. Kazemipour;Ji Liu;Krystyna Solarana;Daniel A. Nagode;P. Kanold;Min Wu;B. Babadi
常见的生物测量是用可能未知和瞬态模糊核的感兴趣信号的噪声卷积的形式。例子包括脑电图和钙成像数据。因此，这些测量的信号反卷积对于理解潜在的生物过程至关重要。本文的目标是从噪声、模糊和欠采样数据中开发快速和稳定的信号反卷积解决方案，其中信号以离散事件的形式分布在时间和空间中。方法：引入可压缩状态空间模型作为框架，对此类离散事件进行建模和估计。这些状态空间模型允许状态突变，具有收敛的转移矩阵，并与压缩线性测量相耦合。我们考虑了一个动态压缩感知优化问题，并开发了一个快速的解决方案，使用两个嵌套的期望最大化算法，共同估计状态及其转移矩阵。在适当的动力学稀疏性假设下，我们证明了状态恢复的最优稳定性保证，并提出了一种具有精确置信范围的识别潜在离散事件的方法。结果：我们进行了模拟研究，并将其应用于钙反褶积和睡眠纺锤体检测，验证了我们的理论结果，并显示出对现有技术的显著改进。结论：我们的研究结果表明，通过明确地模拟底层信号的动态，可以构建可扩展的、统计鲁棒的、高时间分辨率的信号反卷积解决方案。意义：我们提出的方法提供了一个框架，以快速和稳定的方式对噪声、模糊和欠采样的测量进行建模和反卷积，具有广泛的生物数据应用潜力。
Common biological measurements are in the form of noisy convolutions of signals of interest with possibly unknown and transient blurring kernels. Examples include EEG and calcium imaging data. Thus, signal deconvolution of these measurements is crucial in understanding the underlying biological processes. The objective of this paper is to develop fast and stable solutions for signal deconvolution from noisy, blurred and undersampled data, where the signals are in the form of discrete events distributed in time and space. Methods: We introduce compressible state-space models as a framework to model and estimate such discrete events. These state-space models admit abrupt changes in the states and have a convergent transition matrix, and are coupled with compressive linear measurements. We consider a dynamic compressive sensing optimization problem and develop a fast solution, using two nested Expectation Maximization algorithms, to jointly estimate the states as well as their transition matrices. Under suitable sparsity assumptions on the dynamics, we prove optimal stability guarantees for the recovery of the states and present a method for the identification of the underlying discrete events with precise confidence bounds. Results: We present simulation studies as well as application to calcium deconvolution and sleep spindle detection, which verify our theoretical results and show significant improvement over existing techniques. Conclusion: Our results show that by explicitly modeling the dynamics of the underlying signals, it is possible to construct signal deconvolution solutions that are scalable, statistically robust, and achieve high temporal resolution. Significance: Our proposed methodology provides a framework for modeling and deconvolution of noisy, blurred, and undersampled measurements in a fast and stable fashion, with potential application to a wide range of biological data.
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影响因子：
2.5
作者：
Vogelstein, Joshua T.;Packer, Adam M.;Paninski, Liam
通讯作者：
Paninski, Liam
影响因子：
2.5
作者：
Gribonval, Remi;Cevher, Volkan;Davies, Mike E.
通讯作者：
Davies, Mike E.
DOI：
10.1006/meth.1999.0774
发表时间：
1999-06-01
期刊：
METHODS-A COMPANION TO METHODS IN ENZYMOLOGY
影响因子：
--
作者：
Smetters, D;Majewska, A;Yuste, R
通讯作者：
Yuste, R
影响因子：
2.5
作者：
Davies, Mike E.;Eldar, Yonina C.
通讯作者：
Eldar, Yonina C.