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In this latest work, the Newly Modified Robust Tensor Principal Component Analysis (New RTPCA) using affine transformation and L2,1 norms is proposed to remove the outliers and heavy sparse noises in signal processing. This process is done by decomposing the original data matrix as the low-rank heavy sparse noises. The determination of the potential variables is casted as constrained convex optimization problem, and the Alternating Direction Method of Multipliers (ADMM) method is considered to reduce the computational loads in an iterative manner. The simulation results validate the effectiveness of the new method as compared with that of the state-of-the-art methods.

In this study, an effective robust PCA is developed for joint image alignment and recovery via L2,1 norms and affine transformations. To alleviate the potential impacts of outliers, heavy sparse noises, occlusions, and illuminations, the L2,1 norms along with affine transformations are taken into consideration. The determination of the parameters involved and the updating affine transformations is arranged in the form of a constrained convex optimization problem. To reduce the computation load, we also further decompose the error as sparse error and Gaussian noise; additionally, the alternating direction method of multipliers (ADMM) is considered to develop a new set of recursive equations to update the optimization parameters and the affine transformations iterative. The convergence of the derived updating equation is explained as well. Conducted simulations illustrate that the new method is superior to the baseline works in terms of precision on some public databases.

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L∗,w, and the L2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L∗,w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases.