SOME CONCEPTS IN DISCRETE COSINE TRANSFORMS ~ Jennie G. Abraham Fall 2009, EE5355 Under Digital Image and Video Processing files by Dr. Min Wu Please see - lecture10 - Unitary Transform lecture11 - Transform Coding and JPEG Also refer, Fundamentals of Digital Image Processing by A.K. Jain ORTHOGONALITY From last class we, revisit the Orthogonality Property. Unitary vs Orthogonality Unitary matrix: A is unitary if A -1 = A *T = A H – Denote A *T as A H ~ “Hermitian” Orthogonal matrix ~ A -1 = A T – Row vectors of real orthogonal matrix A form orthonormal basis vectors Real-valued unitary matrix is also an orthogonal matrix as is the case with DCT matrix Exercise: Are the matrix here unitary or orthogonal? – If yes, what are the basis vectors ? - = 2 2 1 j j A = 1 1 2 1 2 j j A = 2 1 3 2 3 A - = 2 1 2 1 2 1 2 1 4 A
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SOME CONCEPTS IN DISCRETE COSINE TRANSFORMS
~ Jennie G. Abraham
Fall 2009, EE5355
Under Digital Image and Video Processing files by Dr. Min Wu
Please see -
lecture10 - Unitary Transform
lecture11 - Transform Coding and JPEG
Also refer, Fundamentals of Digital Image Processing by A.K. Jain
ORTHOGONALITY
From last class we, revisit the Orthogonality Property.
Unitary vs Orthogonality
Unitary matrix: A is unitary if A-1 = A*T = AH
– Denote A*T as AH ~ “Hermitian”
Orthogonal matrix ~ A-1 = AT
– Row vectors of real orthogonal matrix A form orthonormal basis vectors
Real-valued unitary matrix is also an orthogonal matrix as is the case with DCT matrix
Exercise: Are the matrix here unitary or orthogonal?