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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 nearinfrared 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.

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In objectbased video representation, video scenes are composed of several arbitrarily shaped video objects (VOs), defined by their texture, shape and motion. In errorprone communications, packet loss results in missing information at the decoder. The impact of transmission errors is minimised through error concealment. In this paper, we propose a spatial error concealment technique for recovering lost shape data. We consider a geometric shape representation consisting of the object boundary, which can be extracted from the -plane. Missing macroblocks result in a broken boundary. A Bspline curve is constructed to replace a missing boundary segment, based on a T spline representation of the received boundary. We use Tsplines because they produce shapepreserving approximations and do not change the characteristics of the original boundary. The representation ensures a good estimation of the first derivatives at the points touching the missing segment. Applying smoothing conditions, we manage to construct a new spline that joins smoothly with the received boundary, leading to successful concealment results. Experimental results on object shapes with different concealment difficulty demonstrate the performance of the proposed method. Comparisons with prior proposed methods are also presented.