A SYSTEM FOR IMAGE COMPRESSION USING WAVELETS AND GENETIC PROGRAMMING
In more recent studies, Genetic Programming has been shown to be useful when used in Image Compression. The major idea is to evolve a set of genetic programs which will output the image, and therefore storing references to this set of programs is needed for decompression. Eventually, it would be possible to find a large set of programs which can be parameterized and used to approximate all possible images. This paper builds upon previous work done in the spatial domain, and instead uses the Discrete Wavelet Packet Transform to simplify the image, and provide better quality levels at better compression ratios. Additionally, quantizing the image in the wavelet domain allows for easier evolution of genetic programs without sacrificing much in terms of image quality. This paper shows with compression ratios of up to 22:1 that genetic programming in the wavelet domain is indeed a feasible method of Image Compression.
Genetic Programming was largely developed by John R. Koza, and has since become useful in many different areas, including biology and physics [4]. Fewer attempts have been made in the area of image processing; however, the use of Genetic Programming in Image Compression is not a new concept [2, 3, 5]. It was suggested in [2] that one could find program representations of an image, and then store the program instead of the actual image data. In [5], Genetic Programming is applied to predictive coding for lossless image compression. The system of compression proposed in [3] segments the image based on complexity, and develops a set of programs which can approximate these segments.
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Genetic Programming begins with the generation of a population of programs which would then evolve to fit a certain set of data. We used a tree structure to represent the functions. In Koza’s work, this proves to be an effective representation of a function which can be easily evolved. Figure 1 shows the tree representation for the expression 2.5 / max(x, 2), which is similar to what is utilized in Koza’s work as an “S-expression” [4]. Each node in the tree represents an operator or a terminal. Terminals are the leaves of the tree, while the operators make up the rest. Terminal Nodes have no children, and are a constant value, or one of the input values. Operator Nodes have a variable amount of children, which depends on the type of operator node. For instance, the “+” operator has 2 children, while the “sin” operator only needs one.
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