From 5b59d4c52d65f4828b650a55e249c539cdb4a39b Mon Sep 17 00:00:00 2001 From: Alex Khrystoforov Date: Sat, 5 Feb 2022 21:39:33 +0200 Subject: [PATCH] Update README.md --- README.md | 30 ++++++++++++++++++++++++++++-- 1 file changed, 28 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 596608c..1bc489b 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,30 @@ -Decomposition into Low-Rank and Sparse Matrices +# Decomposition into Low-Rank and Sparse Matrices +PCP was proposed and developed by Candes et al ( https://arxiv.org/pdf/0912. 3599.pdf ) via an alternating direction methods to solve RPCA problem: -dataset - Carnegie Mellon Test Images Sequences (Y. Sheikh,Robotics Institute, Canergie Mellon University, USA) (1 video, GT images for the se-quence) +minimize | L | ∗ + | S | 1 subject to L + S = M + +where | L | ∗ - is a nuclear norm, | S | 1 - is a L1-norm. + + + +This approach gives good results for recovering low-rank and the sparse matrices in a background (low rank subspace) and foreground (sparse matrix - outliers) separation. But there are some disadvantages of this algorithm: + +• PCP is a very computationally expensive + +• PCP is a batch method (stack training frames in the input), so PCP is inappropriate for real-time subtraction (not incremental way, which would be more useful) + +• PCP imposed the low-rank component being exactly low-rank and sparse component being exactly sparse but the observations such as in video surveillance are ofter corrupted by noise affecting every entry of the data matrix A lot of people are working on different variations of improved algorithms of PCP - incremental algorithms for updating L and S , real-time implementation. Available methods: Modified PCP with Partial Subspace Knowledge, Inductive PCP, PCP with Free Nuclear Norm and so on. + + +## We implemented Principal Component Pursuit by Alternating Directions with following algorithm: +![plot](./PCP-algorithm.png) + +### Results + + + +### Dataset +Carnegie Mellon Test Images Sequences 500frames=25seconds (Y. Sheikh,Robotics Institute, Canergie Mellon University, USA) (1 video, GT images for the se-quence) http://www.cs.cmu.edu/~yaser/new_backgroundsubtraction.htm + +