Dft vs dct in image processing

1. What is the difference between DFT and DCT?
2. Why DCT is used instead of DFT?
3. Is DCT better than DFT?
4. Why DCT is preferred for image processing?

What is the difference between DFT and DCT?

Like the discrete Fourier transform (DFT), a DCT operates on a function at a finite number of discrete data points. The obvious distinction between a DCT and a DFT is that the former uses only cosine functions, while the latter uses both cosines and sines (in the form of complex exponentials).

Why DCT is used instead of DFT?

> DCT is preferred over DFT in image compression algorithms like JPEG > because DCT is a real transform which results in a single real number per > data point. In contrast, a DFT results in a complex number (real and > imaginary parts) which requires double the memory for storage.

Is DCT better than DFT?

We can say DCT is simpler and faster than DFT and also FFT. DCT is suitable for periodically and symmetrically extended sequence whereas DFT is for periodically extended sequence. Therefore DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry.

Why DCT is preferred for image processing?

1) The DCT is real-valued instead of complexity (i.e., it involves magnitude and phase) such that it is easier to be implemented. 2) The DCT is more efficient for illumination variation estimation than the DWT. 3) The DCT approach is similar to the homomorphic filtering, which has been used for contrast enhancement.