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Removing noise from the any processed images is very important. Noise should be removed in such a way that important information of image should be preserved. A decisionbased nonlinear algorithm for elimination of band lines, drop lines, mark, band lost and impulses in images is presented in this paper. The algorithm performs two simultaneous operations, namely, detection of corrupted pixels and evaluation of new pixels for replacing the corrupted pixels. Removal of these artifacts is achieved without damaging edges and details. However, the restricted window size renders median operation less effective whenever noise is excessive in that case the proposed algorithm automatically switches to mean filtering. The performance of the algorithm is analyzed in terms of Mean Square Error [MSE], Peak-Signal-to-Noise Ratio [PSNR], Signal-to-Noise Ratio Improved [SNRI], Percentage Of Noise Attenuated [PONA], and Percentage Of Spoiled Pixels [POSP]. This is compared with standard algorithms already in use and improved performance of the proposed algorithm is presented. The advantage of the proposed algorithm is that a single algorithm can replace several independent algorithms which are required for removal of different artifacts.

We consider the offline constrained reinforcement learning (RL) problem, in which the agent aims to compute a policy that maximizes expected return while satisfying given cost constraints, learning only from a pre-collected dataset. This problem setting is appealing in many real-world scenarios, where direct interaction with the environment is costly or risky, and where the resulting policy should comply with safety constraints. However, it is challenging to compute a policy that guarantees satisfying the cost constraints in the offline RL setting, since the off-policy evaluation inherently has an estimation error. In this paper, we present an offline constrained RL algorithm that optimizes the policy in the space of the stationary distribution. Our algorithm, COptiDICE, directly estimates the stationary distribution corrections of the optimal policy with respect to returns, while constraining the cost upper bound, with the goal of yielding a cost-conservative policy for actual constraint satisfaction. Experimental results show that COptiDICE attains better policies in terms of constraint satisfaction and return-maximization, outperforming baseline algorithms.

A novel distributed control law for consensus of networked double integrator systems with biased measurements is developed in this article. The agents measure relative positions over a time-varying, undirected graph with an unknown and constant sensor bias corrupting the measurements. An adaptive control law is derived using Lyapunov methods to estimate the individual sensor biases accurately. The proposed algorithm ensures that position consensus is achieved exponentially in addition to bias estimation. The results leverage recent advances in collective initial excitation based results in adaptive estimation. Conditions connecting bipartite graphs and collective initial excitation are also developed. The algorithms are illustrated via simulation studies on a network of double integrators with local communication and biased measurements.

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class of distribution-free regularized covariance estimation methods for high-dimensional matrix data under a separability condition and a bandable covariance structure. Under these conditions, the original covariance matrix is decomposed into a Kronecker product of two bandable small covariance matrices representing the variability over row and column directions. We formulate a unified framework for estimating bandable covariance, and introduce an efficient algorithm based on rank one unconstrained Kronecker product approximation. The convergence rates of the proposed estimators are established, and the derived minimax lower bound shows our proposed estimator is rate-optimal under certain divergence regimes of matrix size. We further introduce a class of robust covariance estimators and provide theoretical guarantees to deal with heavy-tailed data. We demonstrate the superior finite-sample performance of our methods using simulations and real applications from a gridded temperature anomalies dataset and a S&P 500 stock data analysis.

Binary pointwise labels (aka implicit feedback) are heavily leveraged by deep learning based recommendation algorithms nowadays. In this paper we discuss the limited expressiveness of these labels may fail to accommodate varying degrees of user preference, and thus lead to conflicts during model training, which we call annotation bias. To solve this issue, we find the soft-labeling property of pairwise labels could be utilized to alleviate the bias of pointwise labels. To this end, we propose a momentum contrast framework (MP2) that combines pointwise and pairwise learning for recommendation. MP2 has a three-tower network structure: one user network and two item networks. The two item networks are used for computing pointwise and pairwise loss respectively. To alleviate the influence of the annotation bias, we perform a momentum update to ensure a consistent item representation. Extensive experiments on real-world datasets demonstrate the superiority of our method against state-of-the-art recommendation algorithms.

In large scale dynamic wireless networks, the amount of overhead caused by channel estimation (CE) is becoming one of the main performance bottlenecks. This is due to the large number users whose channels should be estimated, the user mobility, and the rapid channel change caused by the usage of the high-frequency spectrum (e.g. millimeter wave). In this work, we propose a new hybrid channel estimation/prediction (CEP) scheme to reduce overhead in time-division duplex (TDD) wireless cell-free massive multiple-input-multiple-output (mMIMO) systems. The scheme proposes sending a pilot signal from each user only once in a given number (window) of coherence intervals (CIs). Then minimum mean-square error (MMSE) estimation is used to estimate the channel of this CI, while a deep neural network (DNN) is used to predict the channels of the remaining CIs in the window. The DNN exploits the temporal correlation between the consecutive CIs and the received pilot signals to improve the channel prediction accuracy. By doing so, CE overhead is reduced by at least 50 percent at the expense of negligible CE error for practical user mobility settings. Consequently, the proposed CEP scheme improves the spectral efficiency compared to the conventional MMSE CE approach, especially when the number of users is large, which is demonstrated numerically.

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.

The fact that the millimeter-wave (mmWave) multiple-input multiple-output (MIMO) channel has sparse support in the spatial domain has motivated recent compressed sensing (CS)-based mmWave channel estimation methods, where the angles of arrivals (AoAs) and angles of departures (AoDs) are quantized using angle dictionary matrices. However, the existing CS-based methods usually obtain the estimation result through one-stage channel sounding that have two limitations: (i) the requirement of large-dimensional dictionary and (ii) unresolvable quantization error. These two drawbacks are irreconcilable; improvement of the one implies deterioration of the other. To address these challenges, we propose, in this paper, a two-stage method to estimate the AoAs and AoDs of mmWave channels. In the proposed method, the channel estimation task is divided into two stages, Stage I and Stage II. Specifically, in Stage I, the AoAs are estimated by solving a multiple measurement vectors (MMV) problem. In Stage II, based on the estimated AoAs, the receive sounders are designed to estimate AoDs. The dimension of the angle dictionary in each stage can be reduced, which in turn reduces the computational complexity substantially. We then analyze the successful recovery probability (SRP) of the proposed method, revealing the superiority of the proposed framework over the existing one-stage CS-based methods. We further enhance the reconstruction performance by performing resource allocation between the two stages. We also overcome the unresolvable quantization error issue present in the prior techniques by applying the atomic norm minimization method to each stage of the proposed two-stage approach. The simulation results illustrate the substantially improved performance with low complexity of the proposed two-stage method.

We introduce a novel methodology for particle filtering in dynamical systems where the evolution of the signal of interest is described by a SDE and observations are collected instantaneously at prescribed time instants. The new approach includes the discretisation of the SDE and the design of efficient particle filters for the resulting discrete-time state-space model. The discretisation scheme converges with weak order 1 and it is devised to create a sequential dependence structure along the coordinates of the discrete-time state vector. We introduce a class of space-sequential particle filters that exploits this structure to improve performance when the system dimension is large. This is numerically illustrated by a set of computer simulations for a stochastic Lorenz 96 system with additive noise. The new space-sequential particle filters attain approximately constant estimation errors as the dimension of the Lorenz 96 system is increased, with a computational cost that increases polynomially, rather than exponentially, with the system dimension. Besides the new numerical scheme and particle filters, we provide in this paper a general framework for discrete-time filtering in continuous-time dynamical systems described by a SDE and instantaneous observations. Provided that the SDE is discretised using a weakly-convergent scheme, we prove that the marginal posterior laws of the resulting discrete-time state-space model converge to the posterior marginal posterior laws of the original continuous-time state-space model under a suitably defined metric. This result is general and not restricted to the numerical scheme or particle filters specifically studied in this manuscript.

Deep learning techniques have received much attention in the area of image denoising. However, there are substantial differences in the various types of deep learning methods dealing with image denoising. Specifically, discriminative learning based on deep learning can ably address the issue of Gaussian noise. Optimization models based on deep learning are effective in estimating the real noise. However, there has thus far been little related research to summarize the different deep learning techniques for image denoising. In this paper, we offer a comparative study of deep techniques in image denoising. We first classify the deep convolutional neural networks (CNNs) for additive white noisy images; the deep CNNs for real noisy images; the deep CNNs for blind denoising and the deep CNNs for hybrid noisy images, which represents the combination of noisy, blurred and low-resolution images. Then, we analyze the motivations and principles of the different types of deep learning methods. Next, we compare the state-of-the-art methods on public denoising datasets in terms of quantitative and qualitative analysis. Finally, we point out some potential challenges and directions of future research.