Active Learning for Conditional Generative Compressed Sensing

2026-05-06

AI Summary

This work addresses the challenge of image recovery from limited Fourier measurements by investigating the role of prompt-conditioned generative models in compressive sensing, explicitly distinguishing the dual functions of prompts in both sampling design and reconstruction modeling. The authors propose a prompt-matched Christoffel sampling strategy that integrates ReLU/Lipschitz generators, Stable Diffusion priors, and Fourier subsampling. They theoretically establish that this approach preserves optimal complexity constants and quantify the compatibility penalty incurred by prompt mismatch. Experimental results demonstrate that prompts significantly influence both the sampling distribution and reconstruction quality, thereby validating the effectiveness of the proposed method for stable and efficient image recovery.

Abstract

Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional version of this problem for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. Our framework separates two roles of conditioning: the prompt used to design the sampling distribution and the prompt used to define the recovery model. For ReLU and Lipschitz conditional generators, we prove stable recovery bounds showing that prompt-matched Christoffel sampling retains the same Christoffel complexity constant as existing near-optimal generative compressed sensing theory, while prompt mismatch incurs an explicit compatibility penalty. Experiments with Stable Diffusion show that prompts meaningfully reshape Christoffel sampling distributions and influence image recovery. Overall, our results suggest that prompts should be treated as design variables with distinct effects on sensing, approximation, and recovery.

Problem

• conditional generative compressed sensing
• prompt conditioning
• Christoffel sampling
• image recovery
• prompt mismatch

Innovation

• conditional generative models
• compressed sensing
• active learning
• Christoffel sampling
• prompt conditioning