基于广义主成分分析的图像重建

Image reconstruction based on tensorial principal component analysis

主成分分析(PCA)在图像识别及高维数据降维中有着普遍的应用。为提升基于主成分分析的图像重建性能,在经典PCA算法的基础上提出了广义主成分分析(TPCA),并利用该算法进行图像重建。该算法利用图像像素的空间邻域构成固定尺寸的数组并将其作为广义标量进行代数运算,可以方便有效地描述各像素的空间约束,从而提升图像的重建效果,同时也为其他图像分析算法的改进和升级提供了思路。实验分别将经典PCA算法与TPCA算法运用于公有数据进行图像重建,并对重建质量进行定量分析,结果表明运用TPCA算法的图像重建效果明显优于经典PCA算法。

Principal component analysis(PCA)is widely used in image recognition and dimensionality reduction of high-dimensional data.To improve the performance of PCA for image reconstruction,a generalized principal component analysis algorithm,called tensorial principal component analysis(TPCA),is proposed based on the classical PCA.The TPCA algorithm employs the spatial neighbors of each pixel to form a fixed-sized numerical array which is defined as the corresponding t-scalar for algebraic calculation.Therefore,the TPCA algorithm can effectively characterize the spatial constraints of each pixel and improve the performance of image reconstruction.The approach employed in TPCA also provides a novel perspective for generalizing and improving other image analysis algorithms.In our experiments,PCA and TPCA are respectively applied to public image datasets for image reconstruction.Quantitative performance comparisons for image reconstructions show that TPCA compares favorably to classical PCA in terms of reconstruction quality.