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Introduction to Fourier Analysis of Images Introduction The objective of this laboratory session will be to become familiar with the Fourier transformation of images, and gain experience in using the basic tools for the Fourier analysis of image data using IDL. Following this you will learn how to perform the inverse Fourier transform, and hence be able to perform image enhancement in the spectral domain. The images to be enhanced will possess different types of noise, in this case random and coherent, which require different approaches to remove the noise from the image. Fourier Transform of an Image If we wish to process an image in some way, in order to improve its appearance, there are two ways in which this can be done. One way is in the spatial domain, where we alter the image’s pixels directly in order to change its appearance. The other way is to modify the image in the spectral, or frequency domain, which is the subject of Fourier analysis. Fourier analysis makes the assumption that any image can be constructed by adding together a large number of sinusoidal components of differing frequencies, with each component having its own amplitude. By obtaining the Fourier transform of an image (which can also be represented by an image in the frequency domain), we can get a pictorial representation of the frequency content of an image. This information can then be used, for example, to attenuate the high frequency components of an image, which has the effect of reducing the noise in an image. Exercise 1 The program lab_5a.pro reads an image file and displays its Fourier transform. Run the program to read in the stick1.bmp image. 1/ Describe briefly what the Fourier image is showing. Try to explain why it has particular features. Investigate Fourier transforms of an image with little periodicity, and an image containing some regular features. Briefly describe how the Fourier transforms of these two images relate to the original images and the Fourier…