Advanced Image Compression : Haar Wavelet

Advanced Image Compression: Haar Wavelet Compression is useful because it helps reduce the consumption of expensive resources, such as hard disk space or transmission bandwidth. On the downside, compressed data must be decompressed to be used, and this extra processing may be detrimental to some applications. The design of data compression schemes therefore involves trade-offs among various factors, including the degree of compression, the amount of distortion introduced (if using a lossy compression scheme), and the computational resources required to compress and uncompress the data. A picture can say more than a thousand words. Unfortunately, storing an image can cost more than a million words. This isn't always a problem, because many of today's computers are sophisticated enough to handle large amounts of data. Sometimes however you want to use the limited resources more efficiently. Digital cameras for instance often have a totally unsatisfactory amount of memory, and the internet can be very slow. Wavelet theory intends to analyze and transform data. It can be used to make explicit the correlation between neighboring pixels of an image, and this explicit correlation can be exploited by compression algorithms to store the same image more efficiently. Wavelets can even be used to transform an image in more and less important data items. By only storing the important ones the image can be stored in an amazingly more compact fashion, at the cost of introducing hardly noticeable distortions in the image. In this paper the mathematics behind the compression of images will be outlined. I will treat the basics of data compression, explain what wavelets are, and outline the tricks one can do with wavelets to achieve compression. This paper will also discuss the implementation of the Haar wavelet transform and some of its applications.