Deep Probabilistic Unfolding for Quantized Compressive Sensing

2026-05-11

AI Summary

This work addresses the challenge of balancing reconstruction accuracy and computational efficiency in quantized compressive sensing by proposing a deep unfolding-based probabilistic model. The method reformulates hard quantization constraints into soft, probability-guided priors and introduces a closed-form, numerically stable likelihood gradient projection that aligns with real-world quantization mechanisms. To capture both local and global structures effectively, it incorporates a dual-domain Mamba module that dynamically fuses multi-scale features and models long-range dependencies. Extensive experiments on multiple benchmarks demonstrate that the proposed approach significantly outperforms existing state-of-the-art methods, thereby advancing the practical deployment of quantized compressive sensing.

Abstract

We propose a deep probabilistic unfolding model to address the classical quantized compressive sensing problem that leverages an unfolding framework to enhance the reconstruction accuracy and efficiency. Unlike previous unfolding methods that apply L2 projection to measurements, we derive a closed-form, numerically stable likelihood gradient projection, which allows the model to respect the true quantization physics, turning the hard quantization constraint into a soft probabilistic guidance. Furthermore, an efficient, dual-domain Mamba module is specifically designed to dynamically capture and fuse the multi-scale local and global features, ensuring the interactions between the distant but correlated regions. Extensive experiments demonstrate the state-of-the-art performance of the proposed method over previous works, which is capable of promoting the application of quantized compressive sensing in real life.

Problem

• quantized compressive sensing
• signal reconstruction
• measurement quantization
• inverse problem

Innovation

• probabilistic unfolding
• quantized compressive sensing
• likelihood gradient projection
• dual-domain Mamba
• multi-scale feature fusion