Optical nonsubsampled contourlet transform.

The nonsubsampled contourlet transform (NSCT) is a fully shift-invariant, multiscale, and multidirectional expansion implemented in optics using the Fourier transform of its filters. In this paper, we propose a novel optical NSCT filter design method and the corresponding post-processing method to avoid the use of holographic techniques. The novel optical NSCT filter has real and non-negative Fourier transforms. The input image is placed in the input plane of the VanderLugt 4f correlator, and these real and non-negative Fourier transform NSCT filters are placed in the frequency plane of the VanderLugt 4f correlator. Next, the NSCT result is captured by a CCD in the output plane of the VanderLugt 4f correlator, and its perfect reconstruction is theoretically possible, which is demonstrated by both simulation and optical experiment.