# Wavelets and the Mathematics of Image Compression

## Institution

Western Kentucky University

## Abstract

One of the most often-used but likely least-appreciated applications of mathematics is in the science of image compression. We like for web pages filled with digital images to download quickly -- this does not happen unless the raw data sets from the original images are replaced with equivalent sets of a smaller file size. Our digital cameras and internet browsers encode and decode images for us automatically, using the JPEG format, the current industry standard. However, there is serious mathematics going on in the background. In our poster, we will show a brief summary of the mathematical ideas at work in the JPEG algorithm, and then show how we are getting comparable image compression results using ideas from a branch of mathematics called wavelet theory. The idea is to get smoother and smoother approximations of the original image, keeping track of the error at each step, hopefully generating an equivalent signal with a lot of one character (zeroes). The current JPEG algorithm uses a particular wavelet basis to do this, and we have been working with Dr. Bruce Kessler, Western Kentucky University, to test new multiwavelet bases on digital images.

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Wavelets and the Mathematics of Image Compression

One of the most often-used but likely least-appreciated applications of mathematics is in the science of image compression. We like for web pages filled with digital images to download quickly -- this does not happen unless the raw data sets from the original images are replaced with equivalent sets of a smaller file size. Our digital cameras and internet browsers encode and decode images for us automatically, using the JPEG format, the current industry standard. However, there is serious mathematics going on in the background. In our poster, we will show a brief summary of the mathematical ideas at work in the JPEG algorithm, and then show how we are getting comparable image compression results using ideas from a branch of mathematics called wavelet theory. The idea is to get smoother and smoother approximations of the original image, keeping track of the error at each step, hopefully generating an equivalent signal with a lot of one character (zeroes). The current JPEG algorithm uses a particular wavelet basis to do this, and we have been working with Dr. Bruce Kessler, Western Kentucky University, to test new multiwavelet bases on digital images.