How to design a small-enough dictionary of bases?

[ThTaaa]

Dear Authors,

Thank you for your great work! In your paper (page 7), you mention that the dictionary of base is polynomial in the dimension d (not exponential) and this may help you overcome the "curse of dimensionality". Then you introduce the GAHBs you use in the DNN denoiser. I'm curious how your neural network finds these GAHBs ? Are they selected from a dictionary as you say, and how do you design the small-enough bases dictionary?

Best regards!

[FlorentinGuth]

Hi! In page 7, we are referring to explicit dictionaries that have been constructed by hand. One example is the dictionary of bandlet bases, see e.g. "Geometrical image estimation with orthogonal bandlet bases" by Peyré, G., Le Pennec, E., Dossal, C. & Mallat, S, 2007. For the GAHBs, we do not give a precise definition. They are obtained from the eigenbasis of the Jacobian of the network denoiser. In particular, they are not constrained to be from a dictionary of polynomial size. It is an open question to understand the mathematical properties of these bases, and how DNNs estimate them. Hope this answers your question!