Generalized Image Reconstruction over T-Algebra
This is an incremental improvement for image compression and reconstruction tasks, specifically benefiting applications where spatial data integrity is crucial.
The paper tackles the problem of image reconstruction by addressing the loss of spatial information in PCA due to vectorization, proposing TPCA which uses compounded pixels to preserve correlations, and shows TPCA outperforms PCA with performance improving as the order of compounded pixels increases.
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.