Deep Coupled-Representation Learning for Sparse Linear Inverse Problems with Side Information

In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding of a numerical algorithm into a neural network form, resulting in a substantial reduction of the computational complexity. In this paper, we consider the recovery of a target signal with the aid of a correlated signal, the so-called side information (SI), and propose a deep unfolding model that incorporates SI. The proposed model is used to learn coupled representations of correlated signals from different modalities, enabling the recovery of multimodal data at a low computational cost. As such, our work introduces the first deep unfolding method with SI, which actually comes from a different modality. We apply our model to reconstruct near-infrared images from undersampled measurements given RGB images as SI. Experimental results demonstrate the superior performance of the proposed framework against single-modal deep learning methods that do not use SI, multimodal deep learning designs, and optimization algorithms.