## Problem Set #2

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## Problem Set #2

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- School:
- Massachusetts Institute of Technology
- Course:
- 6 050j - Information and Entropy

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Department of Mechanical Engineering 6 050J 2 110J Information and Entropy Issued February 7 2003 Problem Set 2 Spring 2003 Due February 21 2003 Calendar note This assignment is due two Fridays from lecture since the compression unit is two weeks long Laboratory Experiment This exercise shows you the basis behind compression of images Most video compression codecs today use a form of the Discrete Cosine Transform DCT in their core The DCT separates an image into its spatial frequency components in the x and y directions For example a solid color image will have a DCT with low frequencies while a line drawing image will have a DCT with very high frequencies The transform of an image has the same number of coefficients as the image i e an 8 8 image will have an 8 8 DCT The transform is reversible in the sense that the original image can be recovered exactly from its DCT In MATLAB type dctdemo to view a demonstration of the DCT The following is an explanation of what is happening Clicking on Info will give you a little more information 1 The original image is divided into 8 8 blocks of pixels 2 DCT is applied to each block resulting in an 8 8 block of DCT coefficients The values in the upper left of each block hold the amount of low x and y frequencies and the values in the lower right the amount of high x and y frequencies 3 Compression occurs when small values of the DCT coefficients are set to zero This can be seen by moving the horizontal slider to block out certain values and clicking Apply 4 The dropped small values are set to zero and the inverse DCT used to produce an approximation of the original image The error image is the subtraction of the original pixel values from the reconstructed pixel values When we try to compare the quality of a lossy compression algorithm such as this one qualitative analysis is too subjective Therefore various numerical formulas have

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