Recent development of computational image quality assessment methods has shown to give very promising results in measuring perceptual visual quality for distorted images. However, most of them are difficult to be applied for optimization problems due to the lack of desirable mathematical properties, such as differentiability, convexity, and valid distance metricability. This paper proposes a novel Discrete Cosine Transform (DCT)-based quality degradation metric, called DCT-QM, which is based on the probability summation theory with a psychometric function for neural responses in the receptive fields of visual cortex in psychophysics. Consequently, the DCT-QM is formulated as a weighted mean L-2 norm in the DCT domain, which is very easy to implement and inherits the three desirable mathematical properties, that is, differentiability, convexity, and valid distance metricability, for image quality optimization problems. The extensive experimental results show that the proposed DCT-QM has promising results for many practical distortion types in image processing problems by showing high consistency with perceived visual quality.