Image representation by harmonic transforms with parameters in SL(2,R)SL(2,R)

• New kinds of invariant harmonic transforms with parameters in SL(2,R)SL(2,R) are proposed.
• The capabilities of the proposed PLCT and the 2-D LCTS on image representation are analyzed.

In this paper, a kind of invariant harmonic transforms with parameters in SL(2,R)SL(2,R) are proposed, which include the polar linear canonical transform (PLCT) and the two-dimensional linear canonical transform series (2-D LCTS). The capabilities of the PLCT and the 2-D LCTS on image representation are analyzed. The experimental results show that the 2-D LCTS has much stronger capability on the image representation with respect to characters, and has better invariance of scale and noise than the other transforms. Moreover, due to the varieties of parameters, the performance of the image representation is going bad when parameters used in the reconstructing process are inconsistent with those in the decomposing process. In other words, the proposed transforms can be used for the protection of the image safety because they have free parameters than the traditional methods.