  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.
