h4 - 11 ECE 253a Digital Image Processing Pamela Cosman...

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Unformatted text preview: # 11 ECE 253a Digital Image Processing Pamela Cosman 10/28/11 HOMEWORK 4 Due Friday November 4 in class 1. Scalar Quantization – optimality conditions for squared error distortion Suppose that a random variable X has the two-sided exponential pdf f X ( x ) = λ 2 e- λ | x | A three level quantizer q for X has the form q ( x ) = + b x > a- a ≤ x ≤ + a- b x <- a (a) Find a simple expression for b as a function of a so that the centroid condition is met. (b) For what value of a will the quantizer (using b chosen as above) satisfy the nearest neighbor condition for optimality? 2. Lloyd Algorithm for Quantizer Design A 3-level quantizer is to be designed to minimize mean squared error using the Lloyd algorithm with the training set T = { 1 . , 2 . , 3 . 001 , 4 . , 8 . , 9 . , 12 . } In class, starting with the initial codebook { 1 . , 5 . , 9 . } I found the algorithm con- verges at the codebook { 1 . 5 , 3 . 5 , 9 . 7 } ....
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This note was uploaded on 01/15/2012 for the course ECE ece253A taught by Professor Cosman during the Fall '11 term at UCSD.

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h4 - 11 ECE 253a Digital Image Processing Pamela Cosman...

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