## Abstract

In order to digitally store or send an image there are much better solutions than just describing its dimension in terms of pixels (picture elements) with their color information. The image below is made up of 2560 × 1920 pixels, each one colored with one of the 256 possible gray values. This would give a total of 2560×1920×8 = 39.321.600 bits to represent this image. However, the image in png format uses about half the number of bits by storing it in a more efficient way - this process is called compression.

When the data can be reconstructed faithfully, we call the compression algorithm lossless. In this case, one usually exploits statistical redundancy, which will exist in natural images. Lossy compression, on the other hand, will introduce minor differences in the image, which do not really matter as long as they are undetectable to the human eye. One of the main ways to realize such reconstructions is to express the image as a function and then write it as a linear combination of basic functions of some kind such that most coefficients in the expansion are small (sparse representation). If the basic functions are well chosen, it may be that changing the small coefficients to zero does not change the original function in a visually detectable way.

When the data can be reconstructed faithfully, we call the compression algorithm lossless. In this case, one usually exploits statistical redundancy, which will exist in natural images. Lossy compression, on the other hand, will introduce minor differences in the image, which do not really matter as long as they are undetectable to the human eye. One of the main ways to realize such reconstructions is to express the image as a function and then write it as a linear combination of basic functions of some kind such that most coefficients in the expansion are small (sparse representation). If the basic functions are well chosen, it may be that changing the small coefficients to zero does not change the original function in a visually detectable way.

Original language | English |
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Title of host publication | Optical and Digital Image Processing - Fundamentals and Applications |

Publisher | Wiley VCH |

Pages | 135-154 |

Number of pages | 20 |

ISBN (Print) | 978-3-527-40956-3 |

Publication status | Published - 1 Jan 2011 |

## Keywords

- wavelets