论文标题
用基于得分的生成模型量化压缩感测
Quantized Compressed Sensing with Score-based Generative Models
论文作者
论文摘要
我们考虑从嘈杂的量化测量值中恢复高维信号的总体问题。量化，尤其是粗略的量化，例如1位符号测量值，会导致严重的信息丢失，因此对未知信号的良好先验知识有助于准确恢复。由基于得分的生成模型（SGM，也称为扩散模型）的力量捕获自然信号的丰富结构以外的简单稀疏性，我们提出了一种无人监督的数据驱动方法，称为SGM（QCS-SGM），在此中，先前的分布由预先训练的SGM建模。为了进行后抽样，引入并与先前的SGM分数一起引入了一个称为噪声的伪干样得分的退火伪样分数。提出的QCS-SGM适用于任意数量的量化位。在各种基线数据集上进行的实验表明，提出的QCS-SGM明显优于现有的最新算法，对于分布和分发样品的差距很大。此外，作为一种后抽样方法，QCS-SGM可以轻松地用于获得重建结果的置信区间或不确定性估计。该代码可在https://github.com/mengxiangming/qcs-sgm上找到。
We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.
