Study and applications of the Fourier transform in digital image processing

• Grant number: 14/14348-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2014
• End date: February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Aylton Pagamisse
• Grantee: Ari Teotonio Lopes
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

In this project, we intend to study the theory of Fourier series and Fourier transform, fast Fourier transform, digital images and make applications of the discrete Fourier transform in digital image processing. Initially, the student will study the basic concepts related to Fourier series and their convergence. Then the student will study the continuous Fourier transform and its basic properties. To study the discrete Fourier transform is necessary to make a study of discrete signals and digital images. After this step, the student will study the discrete Fourier transform, the convolution theorem, filtering and fast Fourier transform. From that point will be implemented and tested high pass and low pass filtering of the ideal type, Butterworth and Gaussian. Other applications such as reducing periodic noise and deconvolution of images will also be conducted. The software being used in this project will be Matlab.