Fast Transforms in Image Processing: Compression, Restoration, and Resampling
Table 1
Register of relevant fast transforms, their main characteristic features, and application areas.
ā
Relevance to imaging optics
Main characteristic features
Main application areas
Discrete Fourier Transforms
Represents optical Fourier Transform
Cyclic shift invariance vulnerable to boundary effects
(i) Analysis of periodicities. (ii) Fast convolution and correlation. (iii) Fast and accurate image resampling. (iv) Image compression. (v) Image denoising and deblurring. (vi) Numerical reconstruction of holograms.
Discrete Cosine Transform
Represents optical Fourier Transform
Cyclic shift invariance (with double cycle); virtually not sensitive to boundary effects