Review Article
Fast Transforms in Image Processing: Compression, Restoration, and Resampling
Table 2
Selected fast transforms most relevant for digital image processing and their computational complexity (in 1D denotations).
|
Name |
Definition | Computational complexity | (operations per signal sample) | “Global”: applied to entire signal of
samples | “Local”: applied in mowing window of
pixels |
| Discrete Cosine Transform (DFT) | | Real number operations
| Real number operations
(<WSz) |
| Discrete Fourier Transforms | | | | Canonic DFT | | Complex number operations
| Complex number operations
<WSz | General Shifted Scaled DFT | ; , —shift parameters that indicate shifts , of sampling lattices in signal and spectrum domains;
—sampling scale parameter () |
| Discrete Fresnel Transforms (DFrT) | | | | Canonic DFrT | ; | Complex number operations
| n/a | | Convolutional DFrT | ; |
| Walsh-Hadamard Transform | | | | Hadamard Transform
| ;
| Addition operations only
| n/a | ; ; | Walsh Transform | ; —binary digits of Gray code of taken in bit reversal order |
| Haar Transform (the simplest discrete wavelet transform) | ; —index of the most significant nonzero bit of binary code of msb; —residual of | Addition operations only
| n/a |
|
|