All possible filtering combinations (low- and high-pass) are performed to decompose a matrix or image. The resulting coefficients are associated with a quad-tree structure corresponding to a partitioning of the two-dimensional frequency plane.
dwpt.2d(x, wf="la8", J=4, boundary="periodic")
idwpt.2d(y, y.basis)
a matrix or image containing the data be to decomposed. This ojbect must be dyadic (power of 2) in length in each dimension.
Name of the wavelet filter to use in the decomposition. By default
this is set to "la8", the Daubechies orthonormal compactly
supported wavelet of length \(L=8\) (Daubechies, 1992), least
asymmetric family.
Specifies the depth of the decomposition. This must be a number less than or equal to \(\log(\mbox{length}(x),2)\).
Character string specifying the boundary condition. If
boundary=="periodic" the default, then the vector you
decompose is assumed to be periodic on its defined interval,
if boundary=="reflection", the vector beyond its boundaries
is assumed to be a symmetric reflection of itself.
dwpt.2d object (list-based structure of matrices)
Boolean vector, the same length as \(y\), where
TRUE means the basis tensor should be used in the
reconstruction.
Basically, a list with the following components
Wavelet coefficient matrices (images). The first index is associated with the scale of the decomposition while the second is associated with the frequency partition within that level. The left and right strings, separated by the dash `-', correspond to the first \((x)\) and second \((y)\) dimensions.
Name of the wavelet filter used.
How the boundaries were handled.
The code implements the two-dimensional DWPT using the pyramid algorithm of Mallat (1989).
Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, No. 7, 674-693.
Wickerhauser, M. V. (1994) Adapted Wavelet Analysis from Theory to Software, A K Peters.