A Convergent Neural Network for Non-Blind Image Deblurring

In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling based deep network design since many traditional model-based approaches rely on iterative optimization. Despite exciting progress, typical unrolling approaches heuristically design layer-specific convolution weights to improve performance. Crucially, convergence properties of the underlying iterative algorithm are lost once layer specific parameters are learned from training data. In this paper, we propose a neural network architecture that breaks the trade-off between retaining algorithm properties while simultaneously enhancing performance. We focus on non-blind image deblurring problem and unroll the widely-applied Half-Quadratic Splitting (HQS) algorithm. We develop a new parameterization scheme that enforces the layer-specific parameters to asymptotically approach certain fixed points, a new result that we analytically establish. Experimental results show that our approach outperforms many state of the art non-blind deblurring techniques on benchmark datasets, while enabling convergence and interpretability.