Robust Compressive Sensing Imaging for Quantization Bit Erasure

Existing compressive sensing (CS) reconstruction algorithms are primarily designed for deterministic measurements. However, in real-world scenarios, quantization bit erasures during transmission or storage introduce uncertainty into measurements and significantly complicate reconstruction. We extend the CS framework to explicitly handle such bit-level uncertainty, enabling robust image recovery from quantized measurements with missing bits. We begin by enumerating all valid combinations of the erased quantization bits to construct a candidate set of feasible measurement values. This candidate set is then incorporated as a constraint in a newly formulated inverse problem. We propose an iterative plug-and-play algorithm to solve this problem, alternating between two key steps: (1) an image update using a pretrained denoiser, and (2) a measurement update via a soft-min projection strategy accelerated by coordinate descent. Extensive experiments demonstrate the effectiveness of the proposed approach, achieving high-quality reconstructions even under extremely low sampling rates and severe erasure conditions. Our framework offers a scalable and principled solution for bit-erasure-robust CS reconstruction in error-prone and resource-constrained imaging environments.