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2
X
2
q
where
σ
represents the variance of each input random variable and
σ
denotes the
variance of the quantization error.
8.
Write a program simulating an 8
8 transform coder without quantization. The program
should read the basis set from a file, perform the transform, retain specified coefficients
only, and perform the inverse transform and reconstruction.
(a)
Use this program to compare the discrete cosine transform and the discrete Walsh-
Hadamard transform. Compare the transforms based on objective measures such
as geometric mean and correlation among the coefficients, and by comparing the
quality of the reconstructed image when only the first three and first six coefficients
are retained.
(b)
Finally examine the importance of the DC coefficient by looking at a reconstruction
in which the DC coefficient has been discarded.
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