Fourier Transform Applications: Image Processing Basics

This lecture covers the basics of image processing, including Fourier filters, low-pass and high-pass filters, band-pass filters, Fourier transformation, convolution, cross-correlation, and 3D reconstruction using the Radon projection theorem. It explains how to apply Fourier equations, couple conjugation, and the convolution of images. The instructor demonstrates how to speed up convolution by multiplying FFTs and calculating the inverse FFT. The lecture also discusses the relationship between contrast in images and FFT amplitude, as well as the process of deconvolution. Additionally, it explores the Fourier transform applications in analyzing microscope performance, image resolution, correcting image artifacts, extracting crystal structures, and 3D reconstruction from multiple image orientations.