For a one-dimensional sequence x[n], the autocorrelation matrix is E(xx'), where E is the expectation operator and x' denotes transpose of x[n]. This matrix has Toeplitz structure. If we extend the case for a two-dimensional sequence x[n,m], what is the structure of resulting matrix ?
Any thoughts ?
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I understand that in IP, you first have to do what is called lexicographical ordering. This ordering then makes the autocorrelation matrix as block Toeplitz structure. The usual issue in any DSP/ISP program is to reduce the computational complexity. Matrices are simple to solve if they are diagonalized. Diagonalization is easy to achieve if we perform a similarity transformation. Commonly used is the FFT matrix.
Question is :- What advantages are gained by using FFT over DWT in complexity issues.
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