Low-rank and sparse matrix recovery based on a randomized rank-revealing decomposition

Kaloorazi, Maboud F.; Lamare, Rodrigo C. de

doi:10.1109/icdsp.2017.8096137

Cited by 11 publications

(12 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The work in [3] proposed a rank-revealing decomposition algorithm based on randomized sampling schemes; the matrix A is compressed through pre-and post-multiplication by approximate orthonormal bases for R(A) and R(A T ) obtained via randomization, columns of the reduced matrix and, accordingly, the bases are permuted, the low-rank approximation is then given by projecting the compressed matrix back to the original space. The work in [68] proposed a randomized algorithm termed subspace-orbit randomized SVD (SOR-SVD) to compute a fixed-rank approximation of an input matrix.…”

Section: Outputmentioning

confidence: 99%

“…Such compact representation which retains most important information of a high-dimensional matrix can provide a significant reduction in memory requirements, and more importantly, computational costs when the latter scales, e.g., according to a high-degree polynomial, with the dimensionality. Matrices with low-rank structures have found many applications in background subtraction [1], [2], [3], [4], system identification [5], IP network anomaly detection [6], [7], latent variable graphical modeling, [8], ranking and collaborative filtering, [9], subspace clustering [10], [11], [12], adaptive, sensor and multichannel signal processing [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], biometrics [32], [33], statistical process control and multidimensional fault identification [34], [35], quantum state tomography [36], and DNA microarray data [37]. Singular value decomposition (SVD) [38] and the rankrevealing QR (RRQR) decomposition [39], [40] are among the most commonly used algorithms for computing a lowrank approximation of a matrix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations

Kaloorazi

Lamare

2018

IEEE J. Sel. Top. Signal Process.

Self Cite

View full text Add to dashboard Cite

Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV) decomposition along with a CoR-UTV variant aided by the power method technique. CoR-UTV is primarily developed to compute an approximation to a low-rank input matrix by making use of random sampling schemes. Given a large and dense matrix of size m × n with numerical rank k, where k ≪ min{m, n}, CoR-UTV requires a few passes over the data, and runs in O(mnk) floating-point operations. Furthermore, CoR-UTV can exploit modern computational platforms and, consequently, can be optimized for maximum efficiency. CoR-UTV is simple and accurate, and outperforms reported alternative methods in terms of efficiency and accuracy. Simulations with synthetic data as well as real data in image reconstruction and robust principal component analysis applications support our claims.

show abstract

Section: Outputmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations

Kaloorazi

Lamare

2018

IEEE J. Sel. Top. Signal Process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, the problem of background subtraction was formulated and solved by relying on a low-rank matrix completion framework in Reference [ 69 ]. Furthermore, an efficient rank-revealing decomposition framework based on randomization was presented in Reference [ 70 ] for reconstructions of low-rank and sparse matrices. More researches about RPCA or sparse representation can be found in References [ 71 , 72 , 73 , 74 , 75 ].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Deep Learning Models with Sparse Enhancement Technique for Detection of Newly Grown Tree Leaves

Chen

Lin

et al. 2021

Sensors

View full text Add to dashboard Cite

The life cycle of leaves, from sprout to senescence, is the phenomenon of regular changes such as budding, branching, leaf spreading, flowering, fruiting, leaf fall, and dormancy due to seasonal climate changes. It is the effect of temperature and moisture in the life cycle on physiological changes, so the detection of newly grown leaves (NGL) is helpful for the estimation of tree growth and even climate change. This study focused on the detection of NGL based on deep learning convolutional neural network (CNN) models with sparse enhancement (SE). As the NGL areas found in forest images have similar sparse characteristics, we used a sparse image to enhance the signal of the NGL. The difference between the NGL and the background could be further improved. We then proposed hybrid CNN models that combined U-net and SegNet features to perform image segmentation. As the NGL in the image were relatively small and tiny targets, in terms of data characteristics, they also belonged to the problem of imbalanced data. Therefore, this paper further proposed 3-Layer SegNet, 3-Layer U-SegNet, 2-Layer U-SegNet, and 2-Layer Conv-U-SegNet architectures to reduce the pooling degree of traditional semantic segmentation models, and used a loss function to increase the weight of the NGL. According to the experimental results, our proposed algorithms were indeed helpful for the image segmentation of NGL and could achieve better kappa results by 0.743.

show abstract

“…Therefore, monitoring the health standards of forest ecosystems by remote sensing can alleviate the global warming problem, as climate change may influence phenological events, such as sprouting and senescence [2]. matrix decomposition [40][41][42] have mostly been used for exploratory data analysis and classification in different applications of a variety of scientific and data analytics' problems. Discussion and further analysis have been conducted on the domains of video surveillance [36], subspace tracking [37], anomaly detection [38,42], edge-preserving rain removal [39], automatic target detection [40], burn scar detection [43], blood vessel extraction [44], and cloud removal [45].…”

Section: Introductionmentioning

confidence: 99%

Weighted Background Suppression Target Detection Using Sparse Image Enhancement Technique for Newly Grown Tree Leaves

et al. 2019

View full text Add to dashboard Cite

The process from leaf sprouting to senescence is a phenological response, which is caused by the effect of temperature and moisture on the physiological response during the life cycle of trees. Therefore, detecting newly grown leaves could be useful for studying tree growth or even climate change. This study applied several target detection techniques to observe the growth of leaves in unmanned aerial vehicle (UAV) multispectral images. The weighted background suppression (WBS) method was proposed in this paper to reduce the interference of the target of interest through a weighted correlation/covariance matrix. This novel technique could strengthen targets and suppress the background. This study also developed the sparse enhancement (SE) method for newly grown leaves (NGL), as sparsity has features similar to newly grown leaves. The experimental results suggested that using SE-WBS based algorithms could improve the detection performance of NGL for most detectors. For the global target detection methods, the SE-WBS version of adaptive coherence estimator (SE-WBS-ACE) refines the area under the receiver operating characteristic curve (AUC) from 0.9417 to 0.9658 and kappa from 0.3389 to 0.4484. The SE-WBS version of target constrained interference minimized filter (SE-WBS-TCIMF) increased AUC from 0.9573 to 0.9708 and kappa from 0.3472 to 0.4417; the SE-WBS version of constrained energy minimization (SE-WBS-CEM) boosted AUC from 0.9606 to 0.9713 and kappa from 0.3604 to 0.4483. For local target detection methods, the SE-WBS version of adaptive sliding window CEM (ASW SE-WBS-CEM) enhanced AUC from 0.9704 to 0.9796 and kappa from 0.4526 to 0.5121, which outperforms other methods.

show abstract

Low-rank and sparse matrix recovery based on a randomized rank-revealing decomposition

Cited by 11 publications

References 35 publications

Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations

Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations

Hybrid Deep Learning Models with Sparse Enhancement Technique for Detection of Newly Grown Tree Leaves

Weighted Background Suppression Target Detection Using Sparse Image Enhancement Technique for Newly Grown Tree Leaves

Contact Info

Product

Resources

About