In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.

In image processing, to check a matrix is an of unitary or not, we check the following condition is true or not.

$$W× W*^T = I$$

Where,

W = DFT matrix

W*T = Complex-conjugate transpose of DFT matrix

I = Identity Matrix

The above matrix is not normalized so we compensate and multiple the matrix with 1/N, where N = 4 So, we get

This is called as unitary transformation in Image processing.