ECE468_23 - ECE 468 Digital Image Processing Lecture 22...

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ECE 468: Digital Image Processing Lecture 22 Prof. Sinisa Todorovic [email protected] 1
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Outline Homework 7 due Discrete Wavelet Transform (Textbook 7.3.2) Fast Wavelet Transform (Textbook 7.4) 2
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Discrete Wavelet Transform f ( n ) = 1 M k W ϕ ( j 0 , k ) ϕ j 0 ,k ( n ) + 1 M j = j 0 k W ψ ( j, k ) ψ j,k ( n ) W ϕ ( j 0 , k ) = 1 M n f ( n ) ϕ j 0 ,k ( n ) W ψ ( j, k ) = 1 M n f ( n ) ψ j,k ( n ) , j j 0 M = 2 j n = 0 , 1 , 2 , . . . , M - 1 j = 0 , 1 , 2 , . . . , J - 1 k = 0 , 1 , 2 , . . . , 2 j - 1 3
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Fast Wavelet Transform W ϕ ( j, k ) = 1 M n f ( n ) ϕ j,k ( n ) 4
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Fast Wavelet Transform W ϕ ( j, k ) = 1 M n f ( n ) ϕ j,k ( n ) = 1 M n f ( n )2 j 2 ϕ (2 j n - k ) 4
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Fast Wavelet Transform W ϕ ( j, k ) = 1 M n f ( n ) ϕ j,k ( n ) = 1 M n f ( n )2 j 2 ϕ (2 j n - k ) = 1 M n f ( n )2 j 2 m h ϕ ( m - 2 k ) 2 ϕ (2 j +1 n - m ) 4
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Fast Wavelet Transform W ϕ ( j, k ) = 1 M n f ( n ) ϕ j,k ( n ) = 1 M n f ( n )2 j 2 ϕ (2 j n - k ) = 1 M n f ( n )2 j 2 m h ϕ ( m - 2 k ) 2 ϕ (2 j +1 n - m ) = m h ϕ ( m - 2 k ) 1 M n f ( n )2 j +1 2 ϕ (2 j +1 n - m ) 4
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Fast Wavelet Transform W ϕ ( j, k ) = 1 M n f ( n ) ϕ j,k ( n ) = 1 M n f ( n )2 j 2 ϕ (2 j n - k ) = 1 M n f ( n )2 j 2 m h
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