In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage. This nonlinear quantization process poses significant recovery challenges, particularly with extreme coarse quantization such as 1-bit. Recently, an efficient algorithm called QCS-SGM was proposed for quantized CS (QCS) which utilizes score-based generative models (SGM) as an implicit prior. Due to the adeptness of SGM in capturing the intricate structures of natural signals, QCS-SGM substantially outperforms previous QCS methods. However, QCS-SGM is constrained to (approximately) row-orthogonal sensing matrices as the computation of the likelihood score becomes intractable otherwise. To address this limitation, we introduce an advanced variant of QCS-SGM, termed QCS-SGM+, capable of handling general matrices effectively. The key idea is a Bayesian inference perspective on the likelihood score computation, wherein an expectation propagation algorithm is employed for its approximate computation. We conduct extensive experiments on various settings, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.

翻译：在实际压缩感知（CS）中，获得的测量值在传输或存储前通常需要量化到有限的比特数。这种非线性量化过程带来了显著的恢复挑战，尤其在极端粗糙量化（如1比特）情况下更为突出。近期，针对量化压缩感知（QCS）提出了名为QCS-SGM的高效算法，该算法利用基于分数的生成模型（SGM）作为隐式先验。由于SGM善于捕捉自然信号的复杂结构，QCS-SGM显著优于以往的QCS方法。然而，QCS-SGM仅限于（近似）行正交的感知矩阵，因为其他情况下似然分数的计算变得不可处理。为解决这一局限，我们提出QCS-SGM的进阶变体——QCS-SGM+，该变体能够有效处理通用矩阵。其核心思想是对似然分数计算采用贝叶斯推断视角，并通过期望传播算法实现其近似计算。我们在多种设置下进行了广泛实验，结果表明，对于超越纯行正交性的通用感知矩阵，QCS-SGM+相比QCS-SGM具有显著优越性。