What Is Proper Paper and MATLAB Toolbox Describing and Discussing Wavelet, Ridgelet, Curvelet and Contourlet Transforms in Detail?
On A panorama on multiscale geometric representations, you find a tutorial paper on those directional 2D wavelets, starting with an historical perspective (eg Gaussian &amp; Laplacian pyramids):



and highlighting details between the main fixed and adaptive decompositions (below: a contourlet atom).



It was published in 2011 in Signal processing, special issue on multirate filter banks and multiscale representations. 

It also links to the two-dimensional wavelet and multiscale toolboxes used to generate the figures.