Title: Leveraging Flow-Based Generative Modeling to Refine Sampling Strategies in Compressed Sensing

Abstract:

In contemporary fields such as medical imaging and signal processing, there is a growing demand to capture high-dimensional data while operating under strict resource limitations. Conventional sampling theory dictates that faithful signal reconstruction typically requires a volume of measurements scaling with the signal's ambient dimension, a prerequisite that is frequently prohibitive or unfeasible. Compressed sensing overturns this paradigm by proving that sparse signals can be successfully reconstructed using significantly fewer measurements, assuming the measurement operator satisfies specific criteria.

This proof-of-concept research introduces a task-aware flow-based generative framework, which reimagines the standard Flow Matching training approach. Here, a flow model is specifically trained to optimize subsampling processes within compressed sensing contexts. We validate the fundamental viability of this framework by demonstrating its ability to learn subsampling masks that significantly boost performance across image classification, image reconstruction, and MRI acceleration tasks.

The proposed method achieved state-of-the-art results in image reconstruction, recording a Peak Signal-to-Noise Ratio (PSNR) of 25.17 dB at a 5% subsampling rate on the CelebA dataset. Additionally, it attained a PSNR of 29.24 dB when reconstructing MRI measurements accelerated by a factor of eight using the fastMRI dataset, all while incurring minimal computational costs. These findings underscore the efficacy of integrating task-conditioning into generative flow models and suggest a promising avenue for future representation learning strategies. Ultimately, the framework provides a cohesive and adaptable methodology for creating sensing schemes driven by both data and tasks, with potential applications extending to a wide variety of inverse problems.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC