New models of gray-scale image representation in the 4-D quaternion space are described, wherein images can be processed as quaternion and color images in the frequency domain, by using the concepts of the 2-D quaternion unitary transforms, such as quaternion discrete Fourier transforms, wavelet, and others. Methods of alpha-rooting by such 2-D transforms can be effectively used for gray-scale image enhancement, and optimal parameters enhancements can be found by using the measures EME and EMEC, and image visibility measures of image enhancement. Different models of transferring the gray-scale images into the quaternion space can be applied, which include models 2 × 2, 4 × 1, 4 × 1, and others.