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.

中文翻译：

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T-代数上的广义图像重构

主成分分析（PCA）以其降维和数据压缩功能而闻名。但是，当使用PCA压缩/重建图像时，需要将图像重铸为矢量。图像的矢量化使邻近像素和空间信息丢失产生了一些相关性约束。为了解决PCA采用的矢量化的缺点，我们使用每个像素的较小邻域来形成复合像素，并使用张量版本的PCA（称为TPCA（张量主成分分析））来压缩和重建复合像素的复合图像。我们在公共数据上的实验表明，在压缩和重建图像方面，TPCA与PCA相比具有优势。我们还在实验中表明，当复合像素的顺序增加时，TPCA的性能也会提高。