The idea of any data compression is to find the redundant parts in the available data, for example:
- Temporal redundancy - e.g. For example, there is usually only a minimal difference in the background for two consecutive video images
- Spatial redundancy - points that are spatially closely spaced often have similar coloring
- Spectral redundancy - frequency components can often be `` predicted '' from neighboring components
Wavelet-based methods enable compression rates of the order of 1:65, which are significantly better than previous methods. The theory of wavelets was developed by Yves Meyer at the end of the 1980s and further developed by Ingrid Daubechies and Stéphane Mallat , which resulted in the connections to signal processing.
With the usual wavelet-based compression methods for image data, three main phases can be distinguished:
- Transformation coding : decorrelation of the image data using a 2D wavelet transformation . You get exactly as many coefficients as there are pixels in the image . These coefficients are easier to compress because most of the important information is concentrated in a few coefficients.
- Quantization of the coefficients obtained in the first step.
- Entropy coding or run length coding of the quantized values.
The reconstruction of the image signal is then divided accordingly into decoding, dequantization and inverse transformation.
Wavelet compression in practice
Compared with lossless methods, the compression rates that can be achieved are much higher, and a reduction in the output data by a factor of 65 is definitely feasible.
While the JPEG method tends to `` block '' at higher compression rates (factor 50 and more), such impairments in wavelet-based methods only occur at significantly higher compression rates.
The time required for compression and decompression can be kept within reasonable limits with suitable coding methods. At very high compression rates (reduction by more than a factor of 100), however, algorithms based on fractals can achieve better results than wavelet-based methods.
Examples of wavelet compression