20102ee113_1_EE 113 Project 2010

# 20102ee113_1_EE 113 Project 2010 - Course Project EE 113...

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Course Project EE 113 Spring 2010 DSP in practice: Image Restoration Prepared by Nick Mastronarde and Mihaela van der Schaar 1. Project Summary : The primary purpose of this project is to enable you to further develop your knowledge of digital signal processing techniques by introducing you to basic image filtering principles using Matlab. This project is to be done in groups of up to two students. Each group will submit one project report. Required Files : Several files required for the project are available on the course webpage (eeweb). Specifically, you will need to download: 1. One input image file (lena.bmp). 2. The camera lens degradation function (degradation_func.mat). Matlab Functions : The instructions will specify specific built-in Matlab functions that you will need to use to complete the project. Type “help <function>” in the Matlab command prompt for information on how to use the function. For example, typing “help mean” into the command prompt will provide you information about how to use the function “mean”. You may also search for information about specific functions on the internet. 2. Introduction In this course, you have studied one-dimensional discrete-time sequences ( ) x n , which are indexed by the discrete-time variable n . In this project, instead of working with one- dimensional discrete-time sequences, you will work with images. Images can be represented as two-dimensional M N × sequences ( ) , f x y , where x ( 0 1 x M - ) and y ( 0 1 y N - ) are spatial coordinates, which denote the row and column indices, respectively, of the 2-D image array ( ) , f x y . Many of the computations you are used to performing on 1-D sequences can be extended to 2-D images. Two-dimensional discrete Fourier transform (2-D DFT) The one-dimensional discrete-time Fourier transform describes the frequency content of a one-dimensional signal ( ) x n . Similarly, the two-dimensional discrete Fourier transform describes the frequency content of a two-dimensional signal (or image) ( ) , f x y . An image with smooth color gradients (e.g. an image of a sky at sunset) will have almost all of its energy concentrated in the lower frequency components of the image; in contrast, an image with fine-grained textures (e.g. an image of a forest) or with many edges (e.g. an image of a cathedral) will have significant energy concentrated in the higher frequency components.

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Extension of the one-dimensional discrete Fourier transform and its inverse to two dimensions is straightforward. The discrete Fourier transform of an image ( ) , f x y of size M N × is given by the equation ( ) ( ) ( ) 1 1 2 / / 0 0 1 , , M N j ux M vy N x y F u v f x y e MN π - - - + = = = ∑ ∑ . (1) As in the 1-D case, this expression must be computed for 0,1, , 1 u M = - and 0,1, , 1 v N = - . Similarly, given ( ) , F u v , we obtain ( ) , f x y via the inverse Fourier transform, given by the expression ( ) ( ) ( ) 1 1 2 / / 0 0 1 , , M N j ux M vy N u v f x y F u v e
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## This note was uploaded on 06/01/2010 for the course EE EE113 taught by Professor Mihaela during the Spring '10 term at UCLA.

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20102ee113_1_EE 113 Project 2010 - Course Project EE 113...

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