2D Forward and Inverse Discrete Wavelet Transform¶
Single level dwt2
¶
The relation to the other common data layout where all the approximation and details coefficients are stored in one big 2D array is as follows:
------------------- | | | | cA(LL) | cH(LH) | | | | (cA, (cH, cV, cD)) <---> ------------------- | | | | cV(HL) | cD(HH) | | | | -------------------
PyWavelets does not follow this pattern because of pure practical reasons of simple access to particular type of the output coefficients.
Single level idwt2
¶
2D multilevel decomposition using wavedec2
¶
2D multilevel reconstruction using waverec2
¶
2D coordinate conventions¶
The labels for “horizontal” and “vertical” used by dwt2
and idwt2
follow the common mathematical convention that coordinate axis 0
is horizontal while axis 1 is vertical:
dwt2, idwt2 convention
----------------------
axis 1 ^
|
|
|
|--------->
axis 0
Note that this is different from another common convention used in computer
graphics and image processing (e.g. by matplotlib’s imshow
and functions in
scikit-image
). In those packages axis 0 is a vertical axis and axis 1 is
horizontal as follows:
imshow convention
-------------------
axis 1
|--------->
|
|
|
axis 0 v