# A Low-rank Tensor Dictionary Learning Method for Multi-spectral Images Denoising

## TL;DR

This paper introduces a Low-rank Tensor Dictionary Learning method for denoising multi-spectral images, leveraging shared spatial and spectral dictionaries and nearly low-rank approximations to improve noise removal in real-world data.

## Contribution

The paper proposes a novel LTDL approach that models nearly low-rank structures and learns shared spatial and spectral dictionaries for enhanced MSI denoising.

## Key findings

- Effective denoising on synthetic data
- Superior performance on real MSIs
- Outperforms state-of-the-art methods

## Abstract

As a 3-order tensor, a multi-spectral image (MSI) has dozens of spectral bands, which can deliver more information for real scenes. However, real MSIs are often corrupted by noises in the sensing process, which will further deteriorate the performance of higher-level classification and recognition tasks. In this paper, we propose a Low-rank Tensor Dictionary Learning (LTDL) method for MSI denoising. Firstly, we extract blocks from the MSI and cluster them into groups. Then instead of using the exactly low-rank model, we consider a nearly low-rank approximation, which is closer to the latent low-rank structure of the clean groups of real MSIs. In addition, we propose to learn an spatial dictionary and an spectral dictionary, which contain the spatial features and spectral features respectively of the whole MSI and are shared among different groups. Hence the LTDL method utilizes both the latent low-rank prior of each group and the correlation of different groups via the shared dictionaries. Experiments on synthetic data validate the effectiveness of dictionary learning by the LTDL. Experiments on real MSIs demonstrate the superior denoising performance of the proposed method in comparison to state-of-the-art methods.