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The traditional methods of image assessment, such as mean squared error(MSE), signal-to-noise ratio (SNR), and Peak signal-to-noise ratio (PSNR), areall based on the absolute error of images. Pearson's inner-product correlationcoefficient (PCC) is also usually used to measure the similarity betweenimages. Structural similarity (SSIM) index is another important measurementwhich has been shown to be more effective in the human vision system (HVS).Although there are many essential differences among these image assessments,some important associations among them as cost functions in lineardecomposition are discussed in this paper. Firstly, the selected bases from abasis set for a target vector are the same in the linear decomposition schemeswith different cost functions MSE, SSIM, and PCC. Moreover, for a targetvector, the ratio of the corresponding affine parameters in the MSE-basedlinear decomposition scheme and the SSIM-based scheme is a constant, which isjust the value of PCC between the target vector and its estimated vector.

Associations among Image Assessments as Cost Functions in Linear Decomposition: MSE, SSIM, and Correlation Coefficient