A Novel Adaptive Low-Rank Matrix Approximation Method for Image Compression and Reconstruction

TL;DR

This paper introduces EOD-ABE, an efficient adaptive low-rank matrix approximation method that automatically determines the optimal rank, significantly improving speed and accuracy in image compression and reconstruction tasks.

Contribution

The paper presents a novel orthogonal decomposition method with randomized basis extraction that automatically identifies the optimal rank without additional cost.

Findings

EOD-ABE achieves faster computation with $O(mnr)$ complexity.

It demonstrates superior accuracy and robustness in experiments.

EOD-ABE outperforms existing methods in image compression and hyperspectral data reduction.

Abstract

Low-rank matrix approximation plays an important role in various applications such as image processing, signal processing and data analysis. The existing methods require a guess of the ranks of matrices that represent images or involve additional costs to determine the ranks. A novel efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) is proposed to compute the optimal low-rank matrix approximation with adaptive identification of the optimal rank. By introducing a randomized basis extraction mechanism, EOD-ABE eliminates the need for additional rank determination steps and can compute a rank-revealing approximation to a low-rank matrix. With a computational complexity of $O(mnr)$, where $m$ and $n$ are the dimensions of the matrix and $r$ is its rank, EOD-ABE achieves significant speedups compared to the state-of-the-art methods. Experimental results demonstrate the superior speed, accuracy and robustness of EOD-ABE and indicate that EOD-ABE is a powerful tool for fast image compression and reconstruction and hyperspectral image dimensionality reduction in large-scale applications.