Deep unfolding (or unrolling) bridges the gap between iterative optimization algorithms and neural networks by mapping each algorithmic iteration to a network layer. In signal processing, this approach enables model-based learning that retains interpretability while benefiting from data-driven adaptation. In this article, we introduce the principles of deep unfolding for problems like sparse coding, denoising, and inverse imaging.
We discuss classic iterative algorithms such as ISTA (Iterative Shrinkage-Thresholding Algorithm) and ADMM (Alternating Direction Method of Multipliers) and show how they can be unrolled into trainable neural networks. By learning algorithm parameters directly from data, deep unfolding methods achieve superior performance in tasks like image reconstruction, compressive sensing, and deconvolution while maintaining convergence guarantees from optimization theory. We’ll also highlight recent research and practical applications in radar and communications.