In this paper, a novel technique for the hyperspectral image deconvolution problem is developed. First, considering the highly ill-posed nature of the examined problem, it is imperative to incorporate proper priors (regularizers) to capture the strong spectral and spatial dependencies of the hyperspectral images. Then, in light of this, a novel optimization problem is proposed by employing a convolutional neural network to act as a regularizer, which is learnt to reflect the properties of the signals of interest. To solve the proposed optimization problem, we use the half quadratic splitting methodology, thus designing an efficient iterative solver (iteration map). Based on the Deep Equilibrium (DEQ) modeling, which aims to express the proposed iterative solver as an equilibrium (fixed-point) computation, a highly interpretable deep learning-based network is derived, which can be trained endto-end. Extensive numerical results using two publicly available datasets illustrate that the proposed method markedly outperforms other state-of-the-art approaches.

Considering the high cost of high-resolution Lidar sensors, in this work, a novel Lidar super-resolution method is proposed to improve the performance on numerous autonomous vehicle perception tasks, including that of a Lidar odometer. Specifically, we propose a regularized optimization problem employing a learnable regularizer (neural network) to capture the properties of the data. To efficiently solve this problem, a deep unrolling methodology is proposed, thus forming an interpretable and well-justified deep architecture. Extensive experiments on a real-world lidar odometry application highlight that the proposed model exhibits both superior performance as well as a significantly reduced number of trainable parameters i.e., 99.75% less parameters, as compared to other deep learning methods. The source code used for this work can be found at our repository: repository.

In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local dependencies. A new computationally efficient sparse coding optimization problem is derived by employing regularization terms that are adapted to the properties of the signals of interest. Exploiting the merits of the learnable regularization techniques, a neural network is employed to act as structure prior and reveal the underlying signal dependencies. To solve the optimization problem Deep unrolling and Deep equilibrium based algorithms are developed, forming highly interpretable and concise deep-learning-based architectures, that process the input dataset in a block-by-block fashion. Extensive simulation results, in the context of hyperspectral image denoising, are provided, which demonstrate that the proposed algorithms outperform significantly other sparse coding approaches and exhibit superior performance against recent state-of-the-art deep-learning-based denoising models. In a wider perspective, our work provides a unique bridge between a classic approach, that is the sparse representation theory, and modern representation tools that are based on deep learning modeling.

Given two datasets that belong to different feature spaces and both correspond to the same underlying phenomenon, the scope of coupled dictionary learning is to compute two dictionaries, one for each dataset, so that each dataset is approximated using the respective dictionary but the same sparse coding matrix. In this work, the focus is on a particular, yet widespread, form of this problem in which the datasets correspond to slowly varying (piece-wise smooth) signals, and the measurements contain severe noise. A novel coupled dictionary learning technique is developed by including a suitable total-variation-based regularization term in the cost function. Furthermore, exploiting the smoothness of the datasets, new fast sparse coding algorithms are derived. The new techniques achieve effective modeling of the smooth signal and significantly alleviate the effects of noise. Finally, extensive simulation results for the problem of spectral super-resolution of hyperspectral images are provided, demonstrating the performance improvements offered by the derived techniques.

In recent years, several successful schemes have been proposed to solve the song identification problem. These techniques aim to construct a signal's audio-fingerprint by either employing conventional signal processing techniques or by computing its sparse representation in the time-frequency domain. This paper proposes a new audio-fingerprinting scheme which is able to construct a unique and concise representation of an audio signal by applying a dictionary, which is learnt here via the well-known K-SVD algorithm applied on a song database. The promising results which emerged while conducting the experiments suggested that, not only the proposed approach preformed rather well in its attempt to identify the signal content of several audio clips -even in cases this content had been distorted by noise - but also surpassed the recognition rate of a Shazam-based paradigm.

Distributed estimation of a parameter vector in a network of sensor nodes with ambiguous measurements is considered. The ambiguities are modelled by following a set-theoretic approach, that leads to each sensor employing a non-convex constraint set on the parameter vector. Consensus can be used to reach an estimate consistent with the measurements of all nodes, assuming that such an estimate exists, but unfortunately, such an approach leads to a non-convex problem. Using proper assumptions, the considered problem is decomposed into two sub-problems, where one is well studied in literature and the other is modelled as a non-cooperative game. An exact potential function is derived for this game, and an algorithm for its solution is given. Numerical results, consistent with the theoretical findings, demonstrate the efficacy of the proposed approach.

In this paper, the parameter estimation problem based on diffusion least mean squares strategies is studied from a coalitional game theoretical perspective. The problem has been modeled as a non-transferable coalitional game and two scenarios have been considered, one where the value function includes only a suitable estimation accuracy criterion and another one in which the cost of coalition formation is taken into account as well. In the former scenario, we first analyze the non-emptiness of the core of the games corresponding to traditional diffusion strategies, and then, we extend the analysis to a recently proposed node-specific parameter estimation setting where the nodes have overlapped but different estimation interests. In the latter scenario, we employ a distributed coalition formation algorithm, based on merge-and-split steps, which converges to a stable coalition structure.