DiGCE: Diffusion Model with GRU-Based Conditional Encoder for FRI Signal Reconstruction

Junfeng Cheng, Yingkai Yang, Tania Stathaki

Abstract: The Finite Rate of Innovation (FRI) theory introduces a significant framework in signal processing that charac-terizes classes of signals that can be fully reconstructed from a finite number of samples. This theory suggests that certain non-bandlimited signals can be exactly reconstructed using a limited set of samples, provided these signals have a finite number of degrees of freedom per unit of time. Recently, some researchers have applied learning-based techniques to achieve the goal of FRI signal reconstruction. Although their methods surpass classical reconstruction methods, they still face two critical issues. First, these methods do not perform well when the signals become more complex (e.g., a greater number of sampling points and more pulses for Dirac signals). Secondly, these models have limited generalization ability to different noise levels. To address these challenging issues, we propose DiGCE, a diffusion model with a GRU-based conditional encoder that can achieve high reconstruction quality. In our model, we introduce a GRU-based conditional encoder to better capture the sequential information in complex signals. Moreover, we also leverage the strong signal-denoising capability of the diffusion model, which helps DiGCE better generalize to different noise conditions. Our experiments demonstrate that DiGCE outperforms the existing SOTA baselines.