Two-dimensional wavelet packet coefficients

get_detail2d(M,l,ds) Returns the result of extracting the subband indicated by the string ds of wavelet packet coefficients at level l from the 2-dimensional wavelet packet transform M.

get_smooth2d(M,l) Returns the result of extracting the (0,0)th subband of wavelet packet coefficients at level l from the 2-dimensional wavelet packet transform M.

put_detail2d(M,l,N,ds) Returns the result of inserting the matrix N into the subband indicated by the string ds of wavelet packet coefficients at level l of the 2-dimensional wavelet packet transform M.

put_smooth2d(M,l,N) Returns the result of inserting the matrix N into the index-(0,0) subband of wavelet packet coefficients at level l of the 2-dimensional wavelet packet transform M.

Arguments:

• M is a matrix having at least 2^l rows and columns.
• l is an integer.
• N is a matrix which is the same size as the matrix returned by get_detail2d(M,l,ds) or get_smooth2d(M,l).
• ds is either "H", "V", or "D", and indicates either the index-(1,0), index-(0,1), or index-(1,1) subband.

Notes:

• get_smooth2d(w,l) = get_subband2d(w,l,0,0)
• put_smooth2d(w,l,y) = put_subband2d(w,l,0,0,N)

• get_detail2d(w,l,"H") = get_subband2d(w,l,1,0)
  get_detail2d(w,l,"V") = get_subband2d(w,l,0,1)
  get_detail2d(w,l,"D") = get_subband2d(w,l,1,1)

• put_detail2d(w,l,N,"H") = put_subband2d(w,l,1,0,N)
  put_detail2d(w,l,N,"V") = put_subband2d(w,l,0,1,N)
  put_detail2d(w,l,N,"D") = put_subband2d(w,l,1,1,N)

Mathcad Example

Mathcad Example