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.

翻译：我们考虑从带噪量化测量中恢复高维信号的一般性问题。量化，特别是粗量化如1比特符号测量，会导致严重的信息损失，因此对未知信号的良好先验知识对于精确恢复至关重要。受分数生成模型（SGM，也称为扩散模型）在捕捉自然信号丰富结构（超越简单稀疏性）方面能力的启发，我们提出了一种名为基于SGM的量化压缩感知（QCS-SGM）的无监督数据驱动方法，其中先验分布由预训练的SGM建模。为了进行后验采样，我们引入了一种称为噪声扰动伪似然得分的退火伪似然得分，并将其与SGM的先验得分相结合。所提出的QCS-SGM适用于任意数量的量化比特。在多种基线数据集上的实验表明，对于分布内和分布外样本，所提出的QCS-SGM在性能上大幅优于现有最先进算法。此外，作为一种后验采样方法，QCS-SGM可轻松用于获取重建结果的置信区间或不确定性估计。代码可在 https://github.com/mengxiangming/QCS-SGM 获取。