Mathematics Behind Image Compression: An Experiment of Mean Compression of Various Sizes and Their Relative Compression Ratio of NASA Images

Tanvir Prince^1, , William Ashong-Katai², Ildefonso Salva^3, and Karina M. Shah⁴

¹Assistant Professor of Mathematics Department of Mathematics Hostos Community College The City University of New York USA

²Undergraduate Student Hostos Community College The City University of New York USA

³High School Teacher Department of Mathematics Mott Haven Village Preparatory High School Bronx, New York USA

⁴High School Student The Dalton School New York, USA

Cite this paper:
Tanvir Prince, William Ashong-Katai, Ildefonso Salva and Karina M. Shah. Mathematics Behind Image Compression: An Experiment of Mean Compression of Various Sizes and Their Relative Compression Ratio of NASA Images. International Journal of Data Envelopment Analysis and *Operations Research*. 2014; 1(2):34-39. doi: 10.12691/ijdeaor-1-2-4

Abstract

A study of the fundamentals of image compression was conducted in correspondence with NASA (National Aeronautics and Space Administration). NASA uses images to reveal information, data, and evidence concerning astronomical research. For this reason each NASA image must have the best quality and adequate dimensions. The purpose of this project was to compare the compression ratios resulting from compression by three variations of pixel matrices, and to understand the difference between arithmetic mean and geometric mean compression methods. For this task, a total of 50 planetary images were selected from the NASA website. With the aid of the Mathematica software, the team created a program to compress the images. The team then recorded the findings from the experiment in the form of graphs; visual representation helped to understand the produced trends. The source code for the program is attached in the appendix. This code can be used by anyone who wish to perform and/or repeat the research for a classroom activity or a short project. .

Keywords:
image compression wolfram mathematica NASA Arithmetic mean Geometric mean

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