Analysis and Applications of 2D Discrete Fourier Transform in Image Denoising and Edge Detection
Ziang Li · 2023
The paper explores what is 2 Dimensional Fourier Transform and how it can be used for image processing, specifically denoising and edge enhancing. Starting from the Fourier theorem and Fourier series, the paper traverses through a detailed procedure for the derivation from the 1 dimensional continuous to 1 dimensional discrete to 2 dimensional discrete to 2 dimensional inverse discrete Fourier Transform. After the image is transformed to frequency domain with Fourier transform, highpass and lowpass filters can be applied to edit the information for the purpose of image processing. Such image processing techniques is then implemented on to two examples, a matrix example and an image example, and one accounts for the mathematics approach and another for analyzing the effect of the highpass and lowpass filters, respectively.