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In this paper, we propose an algorithm for recovery of sparse and low-rank components of matrices using an iterative method with adaptive thresholding. In each iteration of the algorithm, the low-rank and sparse components are obtained using a thresholding operator. The proposed algorithm is fast and can be implemented easily. We compare it with the state-of-the-art algorithms. We also apply it to some applications such as background modeling in video sequences, removing shadows and specularities from face images, and image restoration. The simulation results show that the proposed algorithm has a suitable performance with low run-time. © 2017 Elsevier Inc  

Recovering low-rank and sparse components from missing observations is an essential problem in various fields. In this paper, we have proposed a method to address the missing low-rank and sparse decomposition problem. We have used the smoothed nuclear norm and the L1 norm to impose the low-rankness and sparsity constraints on the components, respectively. Furthermore, we have suggested a linear modeling for the corrupted observations. The problem has been solved with the aid of alternating minimization. Moreover, some simplifications have been applied to the relations to reduce the computational complexity, which makes the algorithm suitable for large-scale problems. To evaluate the proposed... 

Similarity measure is an important block in image registration. Most traditional intensity-based similarity measures (e.g., sum-of-squared-difference, correlation coefficient, and mutual information) assume a stationary image and pixel-by-pixel independence. These similarity measures ignore the correlation between pixel intensities; hence, perfect image registration cannot be achieved, especially in the presence of spatially varying intensity distortions. Here, we assume that spatially varying intensity distortion (such as bias field) is a low-rank matrix. Based on this assumption, we formulate the image registration problem as a nonlinear and low-rank matrix decomposition (NLLRMD).... 

In this paper, we propose an Adaptive Singular Value Thresholding (ASVT) for low rank recovery under affine constraints. Unlike previous iterative methods that the threshold level is independent of the iteration number, in our proposed method, the threshold in adaptively decreases during iterations. The simulation results reveal that we get better performance with this thresholding strategy. © 2017 IEEE  

Suppose that a solution x to an underdetermined linear system b=Ax is given. x is approximately sparse meaning that it has a few large components compared to other small entries. However, the total number of nonzero components of x is large enough to violate any condition for the uniqueness of the sparsest solution. On the other hand, if only the dominant components are considered, then it will satisfy the uniqueness conditions. One intuitively expects that x should not be far from the true sparse solution x0. It was already shown that this intuition is the case by providing upper bounds on ||x-x0|| which are functions of the magnitudes of small components of x but independent from x0. In... 

With the dominance of digital imaging systems, we are often dealing with discrete-domain samples of an analog image. Due to physical limitations, all imaging devices apply a blurring kernel on the input image before taking samples to form the output pixels. In this paper, we focus on the reconstruction of binary shape images from few blurred samples. This problem has applications in medical imaging, shape processing, and image segmentation. Our method relies on representing the analog shape image in a discrete grid much finer than the sampling grid. We formulate the problem as the recovery of a rank $r$ matrix that is formed by a Hankel structure on the pixels. We further propose efficient... 

The matrix decomposing into a sum of low-rank and sparse components has found extensive applications in many areas including video surveillance, computer vision, and medical imaging. In this paper, we propose a new algorithm for recovery of low rank and sparse components of a given matrix. We have also proved the convergence of the proposed algorithm. The simulation results with synthetic and real signals such as image and video signals indicate that the proposed algorithm has a better performance with lower run-time than the conventional methods. © 1991-2012 IEEE  

The earlier works in the context of low-rank-sparse-decomposition (LRSD)-driven stationary synthetic aperture radar (SAR) imaging have shown significant improvement in the reconstruction-decomposition process. Neither of the proposed frameworks, however, can achieve satisfactory performance when facing a platform residual phase error (PRPE) arising from the instability of airborne platforms. More importantly, in spite of the significance of real-time processing requirements in remote sensing applications, these prior works have only focused on enhancing the quality of the formed image, not reducing the computational burden. To address these two concerns, this article presents a fast and... 

The binary-valued images usually represent shapes. Therefore, the recovery of binary images from samples is often linked with recovery of shapes, where certain parametric structures are assumed on the shape. In this paper, we study the recovery of shape images with the perspective of low-rank matrix recovery. The matrix of such images is not automatically low-rank. Therefore, we consider the Hankel transformation of binary images in order to apply tools in low-rank matrix recovery. We introduce an ADMM technique for the reconstruction which is numerically confirmed to yield suitable results. We also analyze the sampling requirement of this process based on the theory of random matrices. ©... 

This paper proposes a novel fusion method for visible and infrared images. The infrared and visible samples are obtained by a sampling pattern such as star and spiral. Then, the samples are fused according to fusion rules. Finally, the proposed method is applied to fuse the infrared and visible samples. The proposed method is iterative and a significant advantage of it, besides its superior performance, is that it is faster than the previous compressive sensing based fusion methods. The simulation results confirm the success of the proposed method for fusion of infrared and visible images. © 2018 IEEE  

The problem of extracting low-dimensional structure from high-dimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace, then simple algorithms using linear projections can find the subspace and consequently estimate its dimensionality. However, if the data lies on a low-dimensional but nonlinear space (e.g., manifolds), then its structure may be highly nonlinear and, hence, linear methods are doomed to fail. In this paper, we introduce a new technique for dimensionality reduction based on point-wise operators. More precisely, let $ {bf A} n... 

Similarity measure is a main core of image registration algorithms. Spatially varying intensity distortion is an important challenge, which affects the performance of similarity measures. Correlation among the pixels is the main characteristic of this distortion. Similarity measures such as sum-of-squared-differences (SSD) and mutual information ignore this correlation; hence, perfect registration cannot be achieved in the presence of this distortion. In this paper, we model this correlation with the aid of the low rank matrix theory. Based on this model, we compensate this distortion analytically and introduce rank-regularized SSD (RRSSD). This new similarity measure is a modified SSD based... 

In this paper, we will investigate the efficacy of IMAT (Iterative Method of Adaptive Thresholding) in recovering the sparse signal (parameters) for linear models with random missing data. Sparse recovery rises in compressed sensing and machine learning problems and has various applications necessitating viable reconstruction methods specifically when we work with big data. This paper will mainly focus on comparing the power of Iterative Method of Adaptive Thresholding (IMAT) in reconstruction of the desired sparse signal with that of LASSO. Additionally, we will assume the model has random missing information. Missing data has been recently of interest in big data and machine learning...