Method and apparatus for the compression and decompression of image files using a chaotic system

A system of compressing an image file comprising:

• means for choosing an image file to be compressed and decomposing it into slices;
• means for finding a trend line for each slice and calculating trend line information describing the trend line;
• means for calculating for each slice a detrended image slice, by subtracting from each slice its trend line and storing the trend line information describing the trend line;
• means for choosing a chaotic system;
• means for applying selected digital initialization codes to the chaotic system such that each initialization code produces a periodic orbit and stabilizes the otherwise unstable periodic orbit;
• means for generating a basic waveform for each periodic orbit such that the basic waveform is in a one-to-one correspondence to the initialization code for the periodic orbit;
• means for selecting basic waveforms to be used with each detrended image slice and storing their corresponding initialization codes;
• means for transforming the detrended image slice and the selected basic waveforms to a proper frequency range and storing frequency information describing the transformation;
• means for calculating weighting factors to create a weighted sum of the selected basic waveforms to approximate each detrended image slice and storing the weighting factors;
• and
• means for combining the stored trend line information, the stored initialization codes, the stored frequency information and the stored weighting factors for each detrended image slice to comprise a compressed image file.

A system for compressing an image file comprising:

• a chaotic system;
• a compression controller to apply selected digital initialization codes to the chaotic system to drive in onto periodic orbits and to produce a basic waveform for each periodic orbit that is in a one-to-one correspondence with the initialization code for the periodic orbit;
• an image decomposer to decompose an image to be compressed into slices;
• a slice data detrender to calculate for each slice a detrended image slice by subtracting from each slice its trend line and to store the trend line information;
• a waveform comparator to select the basic waveforms to be used with each detrended image slice and to store their corresponding initialization codes;
• a waveform weighter (i) to transform the detrended image slice and the selected basic waveforms to a proper frequency range and to store frequency information describing the transformation and (ii) to calculate weighting factors to create a weighted sum of the selected basic waveforms to approximate each detrended image slice and to store the weighting factors;
• and
• a storage device to combine the stored trend line information, the stored initialization codes, the stored frequency information and the stored weighting factors for each detrended image slice to comprise a compressed image file.