4 research outputs found
Tensor Robust PCA with Nonconvex and Nonlocal Regularization
Tensor robust principal component analysis (TRPCA) is a promising way for
low-rank tensor recovery, which minimizes the convex surrogate of tensor rank
by shrinking each tensor singular values equally. However, for real-world
visual data, large singular values represent more signifiant information than
small singular values. In this paper, we propose a nonconvex TRPCA (N-TRPCA)
model based on the tensor adjustable logarithmic norm. Unlike TRPCA, our
N-TRPCA can adaptively shrink small singular values more and shrink large
singular values less. In addition, TRPCA assumes that the whole data tensor is
of low rank. This assumption is hardly satisfied in practice for natural visual
data, restricting the capability of TRPCA to recover the edges and texture
details from noisy images and videos. To this end, we integrate nonlocal
self-similarity into N-TRPCA, and further develop a nonconvex and nonlocal
TRPCA (NN-TRPCA) model. Specifically, similar nonlocal patches are grouped as a
tensor and then each group tensor is recovered by our N-TRPCA. Since the
patches in one group are highly correlated, all group tensors have strong
low-rank property, leading to an improvement of recovery performance.
Experimental results demonstrate that the proposed NN-TRPCA outperforms some
existing TRPCA methods in visual data recovery. The demo code is available at
https://github.com/qguo2010/NN-TRPCA.Comment: 19 pages, 7 figure