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arXiv 1802.03056cs.ITmath.IT
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过采样自适应传感

Oversampled Adaptive Sensing

Ralf R. Müller, Ali Bereyhi, Christoph F. Mecklenbräuker

摘要:

我们开发了一个贝叶斯框架的传感,适应感测时间和/或基函数的瞬时感测质量测量的预期后验均方误差。对于稀疏高斯源,与非自适应感测相比,实现了平均感测时间和/或均方误差的显著减少。当压缩比为3、稀疏高斯源为10%、平均感知时间相等时,该方法在多项式时间复杂度的同时,比最优压缩感知的性能提高约2 dB,比非自适应3倍过采样正交感知的性能提高约3 dB,比基于LASSO的恢复方案的性能提高约6 ~ 7 dB。我们利用的是,在高斯噪声的存在下,条件的均方误差对当前的观察是成比例的导数的条件均值估计相对于这个观察。

英文摘要:

We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant reduction in average sensing time and/or mean-squared error is achieved in comparison to non-adaptive sensing. For compression ratio 3, a sparse 10% Gaussian source and equal average sensing times, the proposed method gains about 2 dB over the performance bound of optimum compressive sensing, about 3 dB over non-adaptive 3-fold oversampled orthogonal sensing and about 6 to 7 dB to LASSO-based recovery schemes while enjoying polynomial time complexity. We utilize that in the presence of Gaussian noise the mean-squared error conditioned on the current observation is proportional to the derivative of the conditional mean estimate with respect to this observation.

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