An Image Processing Tour of College Mathematics

An Image Processing Tour of College Mathematics aims to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies.

The topics covered include a library of elementary functions, basic concepts of descriptive statistics, probability distributions of functions of random variables, definitions and concepts behind first- and second-order derivatives,　 most concepts and techniques of traditional linear algebra courses, an introduction to Fourier analysis, and a variety of discrete wavelet transforms - all of that in the context of digital image processing.

• Pre-calculus material and basic concepts of descriptive statistics are reviewed in the context of image processing in the spatial domain.
• Key concepts of linear algebra are reviewed both in the context of fundamental operations with digital images and in the more advanced context of discrete wavelet transforms.
• Some of the key concepts of probability theory are reviewed in the context of image equalization and histogram matching.
• The convolution operation is introduced painlessly and naturally in the context of na ve filtering for denoising and is subsequently used for edge detection and image restoration.
• An accessible elementary introduction to Fourier analysis is provided in the context of image restoration.
• Discrete wavelet transforms are introduced in the context of image compression, and the readers become more aware of some of the recent developments in applied mathematics.
• This text helps students of mathematics ease their way into mastering the basics of scientific computer programming.

Yevgeniy V. Galperin is Associate Professor of Mathematics at East Stroudsburg University of Pennsylvania. He holds a PhD in mathematics and has published several papers in the field of time-frequency analysis and related areas of Fourier analysis. His research and academic interests also include numerical methods, simulation of stochastic processes for real-life applications, and mathematical pedagogy. He has given numerous conference presentations on instructional and course-design approaches directed at increasing student motivation and awareness of societal value of mathematics and on incorporating signal and image processing into the undergraduate mathematics curriculum.