ECE468_22 - ECE 468: Digital Image Processing Lecture 21...

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Unformatted text preview: ECE 468: Digital Image Processing Lecture 21 Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu 1 Outline Wavelet functions (Textbook 7.2.3) Wavelet transform in 1D (Textbook 7.3) 2 Wavelet Function Spaces 3 Scaling Functions j,k ( x ) = 2 j/ 2 (2 j x- k ) Given: ( x ) 4 Wavelet Functions j,k ( x ) = 2 j 2 (2 j x- k ) V j +1 = V j W J j,k ( x ) , j,l ( x ) = 0 5 Any Function If f ( x ) V j 6 Any Function If f ( x ) V j f ( x ) = k k j- 1 ,k ( x ) V j- 1 + k k j- 1 ,k ( x ) V j 6 Any Function If f ( x ) V j f ( x ) = k k j- 2 ,k ( x ) V j- 2 + k k j- 2 ,k ( x ) V j- 1 + k k j- 1 ,k ( x ) V j f ( x ) = k k j- 1 ,k ( x ) V j- 1 + k k j- 1 ,k ( x ) V j 6 Any Function If f ( x ) V j ... f ( x ) = k k j ,k ( x ) + j- 1 l = j k k l,k ( x ) f ( x ) = k k j- 2 ,k ( x ) V j- 2 + k k j- 2 ,k ( x ) V j- 1 + k k j- 1 ,k ( x ) V j f ( x ) = k k j- 1 ,k ( x ) V j- 1 + k k j- 1 ,k ( x ) V j 6 Haar Wavelet Functions f ( x ) = f a ( x ) + f d ( x ) 7 Haar Wavelet Functions f ( x ) = f a ( x ) + f d ( x ) 7 Haar Wavelet Functions Function in V 1 f ( x ) = f a ( x ) + f d ( x ) 7 Haar Wavelet Functions Function in V 1 f ( x ) = f a ( x ) + f d ( x ) 7 Haar Wavelet Functions Function in V 1 Expressed via V f ( x ) = f a ( x ) + f d ( x ) 7 Wavelet Series Expansion...
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ECE468_22 - ECE 468: Digital Image Processing Lecture 21...

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