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首页> 外文期刊>IEEE Transactions on Information Theory >Error Decay of (Almost) Consistent Signal Estimations From Quantized Gaussian Random Projections
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Error Decay of (Almost) Consistent Signal Estimations From Quantized Gaussian Random Projections

机译：量化高斯随机投影的（几乎）一致信号估计的误差衰减

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摘要

This paper provides new error bounds on consistent reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a new observation of the estimated signal under the same sensing model. Focusing on dithered uniform scalar quantization of resolution , we prove first that, given a Gaussian random frame of with vectors, the worst-case -error of consistent signal reconstruction decays with high probability as uniformly for all signals of the unit ball . Up to a log factor, this matches a known lower bound in and former empirical validations in . Equivalently, if exceeds a minimal number of frame coefficients growing like , any vectors in with identical quantized projections are at most apart with high probability. Second, in the context of quantized compressed sensing with Gaussian random measurements and under the same scalar quantization scheme, consistent reconstructions of -sparse signals of have a worst case error that decreases with high probability as uniformly for all such signals. Finally, we show that the proximity of vectors whose quantized random projections are only approximately consistent can still be bounded with high probability. A certain level of corruption is thus allowed in the quantization process, up to the appearance of a systematic bias in the reconstruction error of (almost) consistent signal estimates.
机译：本文为从量化随机投影观察到的信号的一致重建方法提供了新的误差范围。这些信号估计技术可确保在相同的传感模型下，可用量化数据与估计信号的新观测值之间实现完美匹配。着眼于抖动的均匀标量量化量化，我们首先证明，给定具有向量的高斯随机帧，一致信号重构的最坏情况误差对单位球的所有信号均会以高概率衰减。取决于对数因子，它匹配中的已知下界和中的先前经验验证。等效地，如果超过最小数量的像那样增长的帧系数，则具有相同量化投影的任何矢量至多都极有可能分开。第二，在具有高斯随机测量的量化压缩感测的情况下，并且在相同的标量量化方案下，-稀疏信号的一致重建具有最坏情况的误差，该误差对于所有此类信号均以高概率降低。最后，我们证明了其量化的随机投影仅近似一致的向量的邻近度仍可能具有较高的可能性。因此，在量化过程中允许一定程度的损坏，直到在（几乎）一致的信号估计的重建误差中出现系统偏差为止。

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