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Compressive sensing (CS) has recently drawn considerable attentions in signal and image processing communities as a joint sampling and compression approach. Generally, the image CS reconstruction can be formulated as an optimization problem with a properly chosen regularization function based on image priors. In this paper, we propose an efficient image block compressive sensing (BCS) reconstruction method, which combine the best of group-based sparse representation (GSR) model and nonlocal total variation (NLTV) model to regularize the solution space of the image CS recovery optimization problem. Specifically, the GSR model is utilized to simultaneously enforce the intrinsic local sparsity and the nonlocal self-similarity of natural images, while the NLTV model is explored to characterize the smoothness of natural images on a larger scale than the classical total variation (TV) model. To efficiently solve the proposed joint regularized optimization problem, an algorithm based on the split Bregman iteration is developed. The experimental results demonstrate that the proposed method outperforms current state-of-the-art image BCS reconstruction methods in both objective quality and visual perception. [ABSTRACT FROM AUTHOR]

We consider the problem of tensor (i.e., multidimensional array) inpainting in this paper. By using higher-order singular value decomposition, we propose an iterative algorithm that performs soft thresholding on entries of the core tensor and then reconstructs via the directional orthogonal matrices. An inpainted tensor is obtained at the end of the iteration. Simulations conducted over color images, video frames, and MR images validate that the proposed algorithm is competitive with state-of-the-art completion algorithms. The evaluation is made in terms of quality metrics and visual comparison. [ABSTRACT FROM AUTHOR]

In this paper, a variational Bayesian (VB)-based iterative algorithm for ARX models with random missing outputs is proposed. The distributions of missing outputs can be estimated in the VB-E step, and the distributions of unknown parameters can be estimated in the VB-M step by the estimated missing outputs and the available outputs. Compared with the expectation-maximization-based iterative algorithm, this algorithm computes the latent variable and the parameter distributions at each iteration. Therefore, it is more accurate. The simulation results demonstrate the advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In order to accelerate the convergence rate and reduce the steady-state misalignment of the affine projection sign algorithm (APSA), a novel variable step-size APSA based on a posteriori estimation error (APEE) analysis is proposed. The new algorithm modified the iterative process of the APSA in which only sign information of the output error is used. The variable step size is obtained by minimizing the $$L_{2}$$ -norm of the APEE. And the step size has a large value in the initial stage and a small value in the steady state, which can better reflect the working state of the robust adaptive filter than the APSA with fixed step sizes. Therefore, the proposed algorithm achieves a faster convergence and a lower steady-state misalignment than the APSA and its variable step-size versions. The simulation results provided in the paper confirm that the proposed algorithm retains both the advantages of the APSA with large and small step sizes without significantly increase the computational complexity. [ABSTRACT FROM AUTHOR]

Analysis and design of linear periodic control systems are closely related to the discrete-time periodic matrix equations. In this paper, we propose an iterative algorithm based on the conjugate gradient method on the normal equations (CGNE) for finding the solution group of the general coupled periodic matrix equations By proving some properties of the algorithm, we show that the solution group of the periodic matrix equations can be obtained within a finite number of iterations in the absence of roundoff errors. Numerical examples are given to illustrate the efficiency and accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]