Directly Parameterized Neural Network Construction for Generalization and Robustness in Imaging Inverse Problems

Deep learning models achieve state-of-the-art performance in image restoration but remain largely black-box, making it difficult to understand the role of their weights or adapt them to new settings. Algorithm unrolling offers a more principled mechanism to neural network architecture design. In this talk, the presenters will introduce a specific approach to algorithm unrolling via direct parameterization, the Convolutional Dictionary Learning Network (CDLNet). In their approach, they unroll a classical convolutional dictionary learning algorithm into a deep network, ensuring that each layer's operators have a direct correspondence to the original algorithm. They will discuss how this structured design allows CDLNet to achieve competitive results in image denoising and joint denoising-demosaicing while requiring fewer learned parameters than fully convolutional black-box models. Moreover, CDLNet’s interpretability enables the introduction of a noise-adaptive thresholding mechanism, leading to state-of-the-art blind denoising and near-perfect generalization to unseen noise levels. Beyond CDLNet, they will briefly explore how similar interpretability principles extend to architectures incorporating nonlocal self-similarity priors for denoising and compressed sensing MRI reconstruction. By replacing black-box deep models with structured, optimization-inspired networks, these approaches enhance both robustness and generalization, offering a promising path forward for deep learning in inverse problems.