Frequency cosine transform: A bridge between gradient based frequency transform and discrete cosine transform

Discrete cosine transform(DCT) is one of the most powerful tools in image processing. In this paper, we show that each basis of the two dimensional discrete cosine transform (2D-DCT) is an ldquoeigenvectorrdquo of the frequency matrix which is used to obtain basis images of a two dimensional frequency transform (2D-FRT). We also connect the FRT and cosine transform in 1D continuous model. Then, the frequency cosine transform (FCT), is proposed based on the FRT and the DCT. The partial frequency cosine transform (PFCT) is given and discussed in details. It is shown that the FCT can be regarded as a special case of FRT or DCT and it is as sophisticated as the FRT and as fast as the DCT.