Rank Approximation of a Tensor with Applications in Color Image and Video Processing

2019/04/28 by Ramin Goudarzi Karim, Karim, Ramin Goudarzi, Carmeliza Navasca +3
Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1904.12375

openalex publication_date 2019/04/28 · openalex created_date 2019/05/03 · openalex updated_date 2026/08/01

Abstract

We propose a block coordinate descent type algorithm for estimating the rank of a given tensor. In addition, the algorithm provides the canonical polyadic decomposition of a tensor. In order to estimate the tensor rank we use sparse optimization method using ℓ₁ norm. The algorithm is implemented on single moving object videos and color images for approximating the rank.

Citations

• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Most Tensor Problems Are NP-Hard

Related

• Low Rank Approximation of Tensors via Sparse Optimization
• Minimum n-Rank Approximation via Iterative Hard Thresholding
• Tight Lower Bound on the Tensor Rank based on the Maximally Square Unfolding
• Rank-1 Tensor Approximation Methods and Application to Deflation
• Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation