By Thierry Bouwmans, Necdet Serhat Aybat, El-hadi Zahzah
Handbook of sturdy Low-Rank and Sparse Matrix Decomposition: purposes in photo and Video Processing exhibits you ways strong subspace studying and monitoring by way of decomposition into low-rank and sparse matrices supply an appropriate framework for computing device imaginative and prescient functions. Incorporating either latest and new principles, the booklet comfortably provides one-stop entry to a few assorted decompositions, algorithms, implementations, and benchmarking techniques.
Divided into 5 components, the booklet starts off with an total creation to powerful important part research (PCA) through decomposition into low-rank and sparse matrices. the second one half addresses strong matrix factorization/completion difficulties whereas the 3rd half specializes in strong on-line subspace estimation, studying, and monitoring. overlaying purposes in photograph and video processing, the fourth half discusses photograph research, snapshot denoising, movement saliency detection, video coding, key body extraction, and hyperspectral video processing. the ultimate half provides assets and purposes in background/foreground separation for video surveillance.
With contributions from major groups all over the world, this guide presents an entire evaluation of the thoughts, theories, algorithms, and functions on the topic of powerful low-rank and sparse matrix decompositions. it's designed for researchers, builders, and graduate scholars in laptop imaginative and prescient, picture and video processing, real-time structure, laptop studying, and information mining.
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Extra info for Handbook of robust low-rank and sparse matrix decomposition: applications in image and video processing
1. Recursive Projected Compressive Sensing (ReProCS): To address the first two issues, Qiu and Vaswani  proposed an online approach called Recursive Robust PCP (RR-PCP) in , and Recursive Projected Compressive Sensing (ReProCS) in    . The aim of ReProCS is to causally keep updating the sparse matrix St at each time, and keep updating the principal directions. 15) RPCA via Decomposition into Low-Rank and Sparse Matrices: An Overview 1-29 where xt = U T Lt and the matrix U is an unknown m × m orthonormal matrix.
Temporal constraints are addressed by RPCA with dense optical flow , RPCA with consistent optical flow , RPCA with smoothness and arbitrariness constraints  and BRPCA . Only RPCA with smoothness and arbitrariness constraints , BRPCA , and spatio-temporal IRLS  address both the spatial and temporal constraints. ||2,1     ) on the matrices L and/or S, using a structured sparsity norm  on the matrix S, and adding a term in the minimization problem such as a Total Variation penalty     or a gradient     on the matrix S.
Spatial  /-/Spatial /-/-/-/-/-/-/Yes/-/-/-/-/-/-/Spatial , Spatial and temporal /-/Spatial and temporal /-/-/-/-/-/-/ILRSD /Spatial /-/-/-/- Entry-wise noise Quantization error Outliers in entire columns Multimodal backgrounds Outliers in entire columns Outliers in entire columns Entry-wise noise Sparsity control Recovery guarantees Recovery guarantees High intrinsic rank structure Dense outliers Entry-wise noise Entry-wise noise Entry-wise noise Entry-wise noise Entry-wise noise Entry-wise, row-wise, column-wise noise Gaussian noise SPCP Zhou et al.
Handbook of robust low-rank and sparse matrix decomposition: applications in image and video processing by Thierry Bouwmans, Necdet Serhat Aybat, El-hadi Zahzah