  The traditional methods of image assessment, such as mean squared error
(MSE), signal-to-noise ratio (SNR), and Peak signal-to-noise ratio (PSNR), are
all based on the absolute error of images. Pearson's inner-product correlation
coefficient (PCC) is also usually used to measure the similarity between
images. Structural similarity (SSIM) index is another important measurement
which 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 linear
decomposition are discussed in this paper. Firstly, the selected bases from a
basis set for a target vector are the same in the linear decomposition schemes
with different cost functions MSE, SSIM, and PCC. Moreover, for a target
vector, the ratio of the corresponding affine parameters in the MSE-based
linear decomposition scheme and the SSIM-based scheme is a constant, which is
just the value of PCC between the target vector and its estimated vector.
