Listen to your gradients: Integrating gradients into deep unfolding networks

Deep unfolding networks (DUNs) have emerged as competitive networks for compressed sensing (CS) applications that achieve state-of-the-art results while remaining interpretable. Many DUNs adopt the Proximal Gradient Descent DUN (PGD-DUN) proposed by ISTA-Net+. It aims to find a solution to the CS problem that is consistent with the measurements. This is done through a Gradient Descent Module (GDM) to align the output with the measurements, and a deep reconstruction network to enhance the reconstruction performance. However, since the GDM is isolated from the reconstruction network, the network could produce outputs that are misaligned with the measurements, thus, contradicting CS theory. In this work, we show that first, aligning the reconstruction with the measurements plays a critical role in the reconstruction performance. Secondly, we propose the Gradient-Informed Network (GIN) as a superior alternative to GDM. Finally, we show that GIN is generalizable to many PGD-DUNs by applying it to three different PGD-DUNs. The results indicate that GIN consistently outperforms GDM on both the Set 11 and BSD68 datasets and across CS ratios from 50% down to 10%. The results also indicate that the performance seen from GIN increases as the size of the network increases. The codes behind the work will be published upon acceptance of this work. • Demonstrated the importance of minimizing the measurements loss for PGD-DUNs. • Proposed GIN as a superior method to adapt the CS problem to PGD-DUNs compared to GDM. • GIN has a negligible increase in the number of learnable parameters. • Showcased the generalizability of GIN by applying it to three different PGD-DUNs • GIN improved the results of the networks without increasing their computational cost.