How can we calculate the sharpness of an image with discrete cosine transform (DCT) domain? Is it worthy in image quality assessment?
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There is no recipe for such thing.
Moreover, image sharpness is not something well defined.
For instance, homogenous image, is it sharp?
Yet, for what we call real world images we usually have a pretty good prior in the form of distribution of the gradient magnitude (See Why Sparse Priors Like Total Variation Opts to Concentrate Derivatives at a Small Number of Pixels and Any Good Image Blind Deconvolution Algorithm for Removing Camera Shake).
Using that intuition, we can say sharper images might have higher amount of larger magnitude (Namely larger $ b $ parameters in the Laplace Distribution).
The effect of this assumption will be more energy in higher frequencies in the DCT.
Namely you can measure the energy of the higher frequencies bins in your transformation.
To make the metric viable, you need to normalize it somehow. This is usually done in a manner which takes into account the types of images you will be working with.
A good way to start is to look on the energy distribution among the bins.
