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

Abstract

A system for the compression and decompression of image files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of selected basic waveforms is used to approximate each slice of an image. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed image file. When the compressed image file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to produce an approximation of the original image slice.

1 . A method of compressing image data, using a chaotic system, comprising: 
 selecting a subset of the image data;    subtracting a baseline from the image data to form second image data having oscillations about a zero value;    causing the chaotic system to assume periodic orbits by applying initialization codes to the chaotic system;    generating periodic waveforms for the periodic orbits;    weighting the periodic waveforms to approximate at least a portion of the second image data; and    producing a compressed representation of at least the portion of the second image data from a combination of at least one initialization code, a representation of the baseline, and a representation of the weighting.    
     
     
         2 . The method of  claim 1 , wherein the baseline is determined from a least-square regression of the subset of the image data.  
     
     
         3 . The method of  claim 2 , further comprising determining a mathematical model of the baseline.  
     
     
         4 . The method of  claim 3 , wherein the mathematical model includes a spline function.  
     
     
         5 . The method of  claim 1 , further comprising transforming the subset of the second image data and the generated periodic waveforms to a suitable frequency range and storing frequency information describing the transformation, and including the frequency information in the combination of the at least the initialization code, the representation of the baseline, and the representation of the weighting.  
     
     
         6 . The method of  claim 1 , further comprising assigning a weighting of zero to any of the generated periodic waveforms not deemed necessary to approximate sufficiently well the portion of the second image data.  
     
     
         7 . The method of  claim 6 , further comprising removing from a weighted sum of the generated periodic waveforms the initialization code of any periodic waveform having zero weighting.  
     
     
         8 . A method of decompressing a compressed representation of first image data, the compressed representation produced using a first chaotic system and containing a combination of at least an initialization code, a representation of a baseline, and a representation of a weighting, comprising: 
 receiving at a second chaotic system, substantially identical to the first chaotic system, the combination of at least the initialization code, a representation of a baseline, and the representation of a weighting;    causing the second chaotic system to assume periodic orbits by applying the initialization code from the combination;    generating periodic waveforms for the periodic orbits;    applying to the periodic waveforms the weighting; and    adding the baseline to the weighted periodic waveforms to produce second image data substantially identical to at least the portion of the first image data.    
     
     
         9 . The method of  claim 2 , wherein the baseline is represented by a mathematical model.  
     
     
         10 . The method of  claim 9 , wherein the mathematical model includes a spline function.  
     
     
         11 . The method of  claim 8 , comprising back-transforming the second image data and the generated periodic waveforms to an original frequency range based on frequency information received at the second harmonic system, and producing the second image data from the back-transformed image data.