Math 3360: Mathematical Imaging

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Presentation transcript:

Math 3360: Mathematical Imaging Lecture 6: Haar, Walsh & Discrete Fourier Transform Prof. Ronald Lok Ming Lui Department of Mathematics, The Chinese University of Hong Kong

Recap: Haar transform Definition of Haar functions: For details, please refer to Supplementary note 3 Definition of Haar functions:

Recap: Haar transform Definition of Haar transforms: For details, please refer to Supplementary note 3 Definition of Haar transforms: (N = power of 2)

Recap: Walsh transform For details, please refer to Supplementary note 3 Definition of Walsh functions:

Recap: Walsh transform For details, please refer to Supplementary note 3 Definition of Walsh transforms: (N = power of 2)

Haar transform elementary images Haar transform basis image. White = positive; Black = negative; Grey = 0

Walsh transform elementary images Walsh transform basis image. White = positive; Black = negative; Grey = 0

Reconstruction using Haar decomposition = using 1x1 elementary images (first 1 row and first 1 column elementary images; = using 2x2 elementary images (first 2 rows and first 2 column elementary images… And so on…

Error under Haar decomposition

Reconstruction using Walsh decomposition = using 1x1 elementary images (first 1 row and first 1 column elementary images; = using 2x2 elementary images (first 2 rows and first 2 column elementary images… And so on…

Error under Walsh decomposition