Quantized compressed sensing for partial random circulant matrices
Quantized compressed sensing for partial random circulant matrices
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DOI：
10.1109/sampta.2017.8024436
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Joe-Mei Feng;F. Krahmer;Rayan Saab
中科院分区：
文献类型：
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作者：
Joe-Mei Feng;F. Krahmer;Rayan Saab
我们首次对结构化测量产生的压缩感知测量的重要量化方案进行了分析。具体来说，我们的分析研究了压缩感知矩阵，该矩阵由从随机亚高斯向量生成的循环矩阵中随机选择的行组成，无需替换。我们使用稳定的、可能是一位的 Sigma-Delta 方案来量化测量结果，并使用基于凸优化的重建方法。我们表明，由于量化而导致的重建误差部分随测量次数呈多项式衰减。这与与随机高斯或亚高斯矩阵相关的 Sigma-Delta 量化的类似结果一致，并且明显优于与广泛假设的无记忆标量量化相关的结果。
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at random, without replacement, from a circulant matrix generated by a random subgaussian vector. We quantize the measurements using stable, possibly one-bit, Sigma-Delta schemes, and use a reconstruction method based on convex optimization. We show that the part of the reconstruction error due to quantization decays polynomially in the number of measurements. This is in-line with analogous results on Sigma-Delta quantization associated with random Gaussian or subgaussian matrices, and significantly better than results associated with the widely assumed memoryless scalar quantization.