Separating the leading vocals from the musical accompaniment is a challenging task that appears naturally in several music processing applications. Robust principal component analysis (RPCA) has been recently employed to this problem producing very successful results. The method decomposes the signal into a low-rank component corresponding to the accompaniment with its repetitive structure, and...

Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in...

While the performance of Robust Principal Component Analysis (RPCA), in terms of the recovered low-rank matrices, is quite satisfactory to many applications, the time efficiency is not, especially for scalable data. We propose to solve this problem using a novel fast incremental RPCA (FRPCA) approach. The low rank matrices of the incrementally-observed data are estimated using a convex optimiza...

The robust principal component analysis (RPCA) problem seeks to separate lowrank trends from sparse outliers within a data matrix, that is, to approximate a n⇥d matrix D as the sum of a low-rank matrix L and a sparse matrix S. We examine the robust principal component analysis (RPCA) problem under data compression, where the data Y is approximately given by (L+S)·C, that is, a low-rank + sparse...

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose novel non-convex algorithm, coined Iterated CUR (IRCUR), solving RPCA problems, which dramatically improves the computational efficiency in comparison with existing algorithms. IRCUR achieves acceleration by employing decomposition when updating low rank component, allows us to obt...

In this work we develop and study a novel online robust principal components’ analysis (RPCA) algorithm based on the recently introduced ReProCS framework. Our algorithm significantly improves upon the original ReProCS algorithm and it also returns even more accurate offline estimates. The key contribution of this work is a correctness result for this algorithm under relatively mild assumptions...

The research on robust principal component analysis (RPCA) has been attracting much attention recently. The original RPCA model assumes sparse noise, and use the L1-norm to characterize the error term. In practice, however, the noise is much more complex and it is not appropriate to simply use a certain Lp-norm for noise modeling. We propose a generative RPCA model under the Bayesian framework ...

Abstract. The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data ranking. It has been shown that under certain conditions, the solution to the NP-hard RPCA problem can be obtained by solving a convex optimization...

Microscopic image analysis is an important step in biological study. Biologists study the movements of cells under certain drug treatments through a sequence of time-lapse microscopic images to determine the effect of the treatments. The development of modern bright-field microscopes allows more detailed investigations of the cell activities. However, it also brings challenges for automatic cel...