In realistic compressed sensing (CS) scenarios, the obtained measurements usually have to be quantized to a finite number of bits before transmission and/or storage, thus posing a challenge in recovery, especially for extremely coarse quantization such as 1-bit sign measurements. Recently Meng & Kabashima proposed an efficient quantized compressed sensing algorithm called QCS-SGM using the score-based generative models as an implicit prior. Thanks to the power of score-based generative models in capturing the rich structure of the prior, QCS-SGM achieves remarkably better performances than previous quantized CS methods. However, QCS-SGM is restricted to (approximately) row-orthogonal sensing matrices since otherwise the likelihood score becomes intractable. To address this challenging problem, in this paper we propose an improved version of QCS-SGM, which we call QCS-SGM+, which also works well for general matrices. The key idea is a Bayesian inference perspective of the likelihood score computation, whereby an expectation propagation algorithm is proposed to approximately compute the likelihood score. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM+ outperforms QCS-SGM by a large margin when sensing matrices are far from row-orthogonal.

翻译：在实际压缩感知场景中，通常需要在传输和/或存储前将所得测量值量化为有限比特数，这给信号恢复带来了挑战，尤其是在1比特符号测量等极端粗量化条件下。近期，Meng与Kabashima利用基于分数的生成模型作为隐式先验，提出了一种高效量化压缩感知算法QCS-SGM。得益于分数生成模型在捕捉先验丰富结构方面的强大能力，QCS-SGM在性能上显著优于现有量化压缩感知方法。然而，QCS-SGM仅适用于（近似）行正交感知矩阵，否则其似然分数将难以处理。为解决这一难题，本文提出QCS-SGM的改进版本——QCS-SGM+，该算法在一般感知矩阵下同样表现优异。其核心思想是基于贝叶斯推理视角进行似然分数计算，通过提出期望传播算法来近似计算似然分数。在多种基线数据集上的实验表明，当感知矩阵远离行正交条件时，所提出的QCS-SGM+在性能上大幅超越QCS-SGM。