Generalized Image Reconstruction over T-Algebra

TL;DR

This paper introduces TPCA, a tensor-based PCA method that improves image compression and reconstruction by preserving spatial information through compounded pixels, outperforming traditional PCA.

Contribution

The paper proposes a tensorial PCA approach that maintains spatial pixel relationships, enhancing image compression and reconstruction over standard PCA.

Findings

TPCA outperforms PCA in image compression and reconstruction.

Increasing the order of compounded pixels improves TPCA performance.

Experiments on public data validate the effectiveness of TPCA.

Abstract

Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, images need to be recast to vectors. The vectorization of images makes some correlation constraints of neighboring pixels and spatial information lost. To deal with the drawbacks of the vectorizations adopted by PCA, we used small neighborhoods of each pixel to form compounded pixels and use a tensorial version of PCA, called TPCA (Tensorial Principal Component Analysis), to compress and reconstruct a compounded image of compounded pixels. Our experiments on public data show that TPCA compares favorably with PCA in compressing and reconstructing images. We also show in our experiments that the performance of TPCA increases when the order of compounded pixels increases.