Generalized Image Reconstruction over T-Algebra

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 compoun pixels and use a tensorial version of PCA, called TPCA (Tensorial Principal Component Analysis), to compress and reconstruct a compound image of compound 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 compound pixels increases.