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

## TL;DR

This paper introduces a block coordinate descent algorithm that estimates tensor rank and provides its canonical polyadic decomposition, with applications demonstrated on color images and videos.

## Contribution

The paper presents a novel sparse optimization-based algorithm for tensor rank estimation and decomposition, applicable to image and video processing.

## Key findings

- Effective tensor rank estimation on color images and videos
- Successful application of the algorithm to real-world visual data
- Demonstrated improvement over existing methods in tensor approximation

## 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 $\ell_1$ norm. The algorithm is implemented on single moving object videos and color images for approximating the rank.