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This paper considers online robust principal component analysis (RPCA) in time-varying decomposition problems such as video foreground-background separation. We propose a compressive online RPCA algorithm that decomposes recursively a sequence of data vectors (e.g., frames) into sparse and low-rank components. Different from conventional batch RPCA, which processes all the data directly, our approach considers a small set of measurements taken per data vector (frame). Moreover, our algorithm can incorporate multiple prior information from previous decomposed vectors via proposing an $n$ - $\ell _{1}$ minimization method. At each time instance, the algorithm recovers the sparse vector by solving the $n$ - $\ell _{1}$ minimization problem—which promotes not only the sparsity of the vector but also its correlation with multiple previously recovered sparse vectors—and, subsequently, updates the low-rank component using incremental singular value decomposition. We also establish theoretical bounds on the number of measurements required to guarantee successful compressive separation under the assumptions of static or slowly changing low-rank components. We evaluate the proposed algorithm using numerical experiments and online video foreground-background separation experiments. The experimental results show that the proposed method outperforms the existing methods. [ABSTRACT FROM AUTHOR]

Contrastive learning has revolutionized the field of computer vision, learning rich representations from unlabeled data, which generalize well to diverse vision tasks. Consequently, it has become increasingly important to explain these approaches and understand their inner workings mechanisms. Given that contrastive models are trained with interdependent and interacting inputs and aim to learn invariance through data augmentation, the existing methods for explaining single-image systems (e.g., image classification models) are inadequate as they fail to account for these factors and typically assume independent inputs. Additionally, there is a lack of evaluation metrics designed to assess pairs of explanations, and no analytical studies have been conducted to investigate the effectiveness of different techniques used to explaining contrastive learning. In this work, we design visual explanation methods that contribute towards understanding similarity learning tasks from pairs of images. We further adapt existing metrics, used to evaluate visual explanations of image classification systems, to suit pairs of explanations and evaluate our proposed methods with these metrics. Finally, we present a thorough analysis of visual explainability methods for contrastive learning, establish their correlation with downstream tasks and demonstrate the potential of our approaches to investigate their merits and drawbacks. [ABSTRACT FROM AUTHOR]

In the context of low-cost video encoding, distributed video coding (DVC) has recently emerged as a potential candidate for uplink-oriented applications. This paper builds on a concept of correlation channel (CC) modeling, which expresses the correlation noise as being statistically dependent on the side information (SI). Compared with classical side-information-independent (SII) noise modeling adopted in current DVC solutions, it is theoretically proven that side-information-dependent (SID) modeling improves the Wyner–Ziv coding performance. Anchored in this finding, this paper proposes a novel algorithm for online estimation of the SID CC parameters based on already decoded information. The proposed algorithm enables bit-plane-by-bit-plane successive refinement of the channel estimation leading to progressively improved accuracy. Additionally, the proposed algorithm is included in a novel DVC architecture that employs a competitive hash-based motion estimation technique to generate high-quality SI at the decoder. Experimental results corroborate our theoretical gains and validate the accuracy of the channel estimation algorithm. The performance assessment of the proposed architecture shows remarkable and consistent coding gains over a germane group of state-of-the-art distributed and standard video codecs, even under strenuous conditions, i.e., large groups of pictures and highly irregular motion content. [ABSTRACT FROM AUTHOR]

Deep unfolding methods design deep neural networks as learned variations of optimization algorithms through the unrolling of their iterations. These networks have been shown to achieve faster convergence and higher accuracy than the original optimization methods. In this line of research, this paper presents novel interpretable deep recurrent neural networks (RNNs), designed by the unfolding of iterative algorithms that solve the task of sequential signal reconstruction (in particular, video reconstruction). The proposed networks are designed by accounting that video frames’ patches have a sparse representation and the temporal difference between consecutive representations is also sparse. Specifically, we design an interpretable deep RNN (coined reweighted-RNN) by unrolling the iterations of a proximal method that solves a reweighted version of the $\ell _{1}$ - $\ell _{1}$ minimization problem. Due to the underlying minimization model, our reweighted-RNN has a different thresholding function (alias, different activation function) for each hidden unit in each layer. In this way, it has higher network expressivity than existing deep unfolding RNN models. We also present the derivative $\ell _{1}$ - $\ell _{1}$ -RNN model, which is obtained by unfolding a proximal method for the $\ell _{1}$ - $\ell _{1}$ minimization problem. We apply the proposed interpretable RNNs to the task of video frame reconstruction from low-dimensional measurements, that is, sequential video frame reconstruction. The experimental results on various datasets demonstrate that the proposed deep RNNs outperform various RNN models. [ABSTRACT FROM AUTHOR]

The reconstruction of a high resolution image given a low resolution observation is an ill-posed inverse problem in imaging. Deep learning methods rely on training data to learn an end-to-end mapping from a low-resolution input to a high-resolution output. Unlike existing deep multimodal models that do not incorporate domain knowledge about the problem, we propose a multimodal deep learning design that incorporates sparse priors and allows the effective integration of information from another image modality into the network architecture. Our solution relies on a novel deep unfolding operator, performing steps similar to an iterative algorithm for convolutional sparse coding with side information; therefore, the proposed neural network is interpretable by design. The deep unfolding architecture is used as a core component of a multimodal framework for guided image super-resolution. An alternative multimodal design is investigated by employing residual learning to improve the training efficiency. The presented multimodal approach is applied to super-resolution of near-infrared and multi-spectral images as well as depth upsampling using RGB images as side information. Experimental results show that our model outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]