2023/02/02 by Xiangming Meng, Meng, Xiangming, Yoshiyuki Kabashima +1 · 1 citation
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Machine Learning (cs.LG) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2302.00919
openalex publication_date 2023/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 expectation propagation is employed for its approximate computation. Extensive experiments are conducted, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.