Programming the IDWT for image processing I want to program the 2D inverse discrete wavelet transform (only 1 level) in the case of image processing. In the matlab website there's this diagram:


now, I want to program the IDWT with haar wavelets. What are the kernels of the low pass filter and the high pass filters?
here is one version of the Haar analysis/synthesis filter bank pair. Oddly, the synthesis filters, up to a scale factor, are mirrors of  the analysis filters.

Other options are:


$\pm 1/\sqrt{2}$ instead or $1/2$ and $1$ (orthogonal version);
reverse: $[1 \;  \pm 1]$ at analysis and $[\pm 1/2 \; 1/2]$ at the synthesis.