[Paper Review] Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing

Vishal Monga, Yuelong Li+1 more|arXiv (Cornell University)|Dec 22, 2019

Sparse and Compressive Sensing Techniques43 citations

TL;DR

The paper surveys algorithm unrolling (unfolding) as a principled way to convert iterative signal processing algorithms into trainable, interpretable deep networks, with efficiency and generalization benefits.

ABSTRACT

Deep neural networks provide unprecedented performance gains in many real world problems in signal and image processing. Despite these gains, future development and practical deployment of deep networks is hindered by their blackbox nature, i.e., lack of interpretability, and by the need for very large training sets. An emerging technique called algorithm unrolling or unfolding offers promise in eliminating these issues by providing a concrete and systematic connection between iterative algorithms that are used widely in signal processing and deep neural networks. Unrolling methods were first proposed to develop fast neural network approximations for sparse coding. More recently, this direction has attracted enormous attention and is rapidly growing both in theoretic investigations and practical applications. The growing popularity of unrolled deep networks is due in part to their potential in developing efficient, high-performance and yet interpretable network architectures from reasonable size training sets. In this article, we review algorithm unrolling for signal and image processing. We extensively cover popular techniques for algorithm unrolling in various domains of signal and image processing including imaging, vision and recognition, and speech processing. By reviewing previous works, we reveal the connections between iterative algorithms and neural networks and present recent theoretical results. Finally, we provide a discussion on current limitations of unrolling and suggest possible future research directions.

Motivation & Objective

• Motivate the need for interpretable, generalizable deep networks in signal and image processing.
• Explain the algorithm unrolling framework that maps iterative algorithms to neural networks.
• Show how unrolled networks encode domain knowledge and reduce data requirements.
• Survey applications across imaging, vision, and medical imaging.
• Discuss limitations and future research directions.

Proposed method

• Describe the unrolling procedure where each iteration of an algorithm becomes a network layer.
• Learn layer-specific parameters end-to-end via back-propagation to optimize performance.
• Illustrate with Learned ISTA (LISTA) where ISTA iterations are unrolled into a trainable network.
• Generalize the approach to other iterative schemes and show parameter sharing vs. layer-wise variation.
• Highlight how unrolled networks are more interpretable and parameter-efficient than generic networks.

Experimental results

Research questions

• RQ1 How can iterative signal processing algorithms be translated into trainable neural networks through unrolling?
• RQ2 What are the interpretability, efficiency, and generalization benefits of unrolled networks compared to traditional deep nets?
• RQ3 Which applications in imaging, vision, and medical imaging benefit from algorithm unrolling, and why?
• RQ4 What theoretical results exist on convergence and learned parameters for unrolled architectures?
• RQ5 What are open challenges and future directions for algorithm unrolling?

Key findings

• Unrolled networks provide a parameter-efficient alternative to generic neural networks by embedding domain knowledge from iterative algorithms.
• LISTA demonstrates that learned ISTA can reach similar performance with far fewer layers (iterations) and faster convergence.
• Unrolling extends beyond sparse coding to diverse problems such as image deblurring, super-resolution, and medical imaging reconstruction.
• Networks derived from unrolling can achieve competitive or superior performance with fewer training samples due to structured priors.
• The approach yields faster inference and interpretable architectures linked to the underlying algorithmic steps.