# Generalized Image Reconstruction over T-Algebra

arXiv: https://arxiv.org/abs/2101.06650 · HTML: https://mlsanity.com/paper/2101.06650/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 8 references that are in the map.
- First posted on arXiv 17 Jan 2021.

## Builds on (most cited first, 2 of 2)

- [Generalized Visual Information Analysis via Tensorial Algebra](https://mlsanity.com/paper/2001.11708/) (2020)
- [General Data Analytics with Applications to Visual Information Analysis: A Provable Backward-Compatible Semisimple Paradigm over T-Algebra](https://mlsanity.com/paper/2011.00307/) (2020)

## Built on by (most cited first, 2 of 2)

- [Principal Bit Analysis: Autoencoding with Schur-Concave Loss](https://mlsanity.com/paper/2106.02796/) (2021)
- [Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra](https://mlsanity.com/paper/2202.00450/) (2022)

## Abstract (arXiv)

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.