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Types of Coding
Source Coding - statute entropy to more ef?ciently represent the information Reduces size of it of information Analog - Encode latitude source data into a binary format Digital - Reduce the size of digital source data Channel Coding - Code data for transmition over a noisy communication channel Increases size of data Digital - add redundancy to identify and remedy errors Analog - represent digital values by analog signals Complete Information Theory was developed by Claude Shannon
C. A. Bouman: Digital Image touch on - January 7, 2007
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Digital Image Coding
Images from a 6 MPixel digital cammera are 18 MBytes each Input and outfit images are digital Output image must be smaller (i.e. ? 500 kBytes) This is a digital source steganography problem
C. A. Bouman: Digital Image Processing - January 7, 2007
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Two Types of Source (Image) Coding
lossless code (entropy coding) Data can be decoded to form on the nose the same bits Used in zip flock solely achieve moderate compression (e.g. 2:1 3:1) for natural images Can be important in definite applications such as medical imaging Lossly source coding Decompressed image is visually similar, but has been changed Used in JPEG and MPEG Can achieve much greater compression (e.g.
20:1 40:1) for natural images Uses entropy coding
C. A. Bouman: Digital Image Processing - January 7, 2007
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Entropy
Let X be a random variables pickings values in the pin down {0, · · · , M ? 1} such that pi = P {X = i} Then we de?ne the entropy of X as H(X) = ?
M ?1 i=0
pi log2 pi
= ?E [log2 pX ] H(X) has units of bits
C. A. Bouman: Digital Image Processing - January 7, 2007
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Conditional Entropy and Mutual Information
Let (X, Y ) be a random variables taking values in the set {0, · · · , M ? 1}2 such that p(i, j) = P {X = i, Y = j} p(i|j) = p(i, j) M ?1 k=0 p(k, j)
M ?1 M ?1 i=0 j=0
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