A Steerable Complex Wavelet Construction and Its Application to Image Denoising

This work addresses the design of a novel complex steerable wavelet construction, the generation of transform-space feature measurements associated with corner and edge presence and orientation properties, and the application of these measurements directly to image denoising. The decomposition uses pairs of bandpass filters that display symmetry and antisymmetry about a steerable axis of orientation. While the angular characterization of the bandpass filters is similar to those previously described, the radial characteristic is new, as is the manner of constructing the interpolation functions for steering. The complex filters have been engineered into a multirate system, providing a synthesis and analysis subband filtering system with good reconstruction properties. Although the performance of our proposed denoising strategy is currently below that of recently reported state-of-the-art techniques in denoising, it does compare favorably with wavelet coring approaches employing global thresholds and with an “Oracle” shrinkage technique, and presents a very promising avenue for exploring structure-based denoising in the wavelet domain.