Dual Tree Complex Shearlet Transform and its Shift Invariance Properties

In Shearlab, the publicized spatial implementation of Shearlet Transform is shift-variance because it is based on DWT, which is shift-variance. The deficiency of the spatial implementation scheme could be mitigated by the method of Dual Tree Complex Shearlet Transform (DT CST). In this paper, the definition of Complex Shearlet Transform is given, and then discussed the details of the DT CST about its theory, structure and implementation. Numerical results suggest that it is nearly shift-invariance.