Dual-Tree Cosine-Modulated Filter Bank With Linear-Phase Individual Filters: An Alternative Shift-Invariant and Directional-Selective Transform

Dual-tree transforms have recently received much attention for the properties of shift-invariance and directional-selectivity. However, their designs generally encounter fractional-delay constraints, and become more complicated for providing linear-phase (LP) individual filters and flexible directional-selectivity, two important properties in image processing. In this paper, we propose an alternative shift-invariant and directional-selective transform-the dual-tree cosine-modulated filter bank (DTCMFB). In the proposed DTCMFB, its primal and dual filter banks are derived by cosine-modulating one LP prototype filter, and thus its design involves no fractional-delay constraints. Meanwhile, the derived modulation technique guarantees each individual filter to be LP and the LP condition is satisfied without any constraint on the prototype filter. By separable operations, the DTCMFB is extended to two-dimensions. The resulting 2D DTCMFB can provide much more flexible directional-selectivity. Finally, several simulations are given to verify the proposed DTCMFB, and the experiments on nonlinear approximation and image denoising are presented to demonstrate its potential in image processing.