A Nonlinear Steerable Complex Wavelet Decomposition of Images

Signal and image representations that are steerable are essential to capture efficiently directional features. However, those that are successful at achieving directional selectivity usually use too many subbands, resulting in low computational efficiency. In this paper, we propose a two-dimensional nonlinear transform that uses only two subbands to achieve rotation invariance property, and enjoys a mirror reconstruction making it similar to a "tight frame". The two-subband structure is merged into a unique, concise, complex-valued subband that approximates a Wirtinger gradient which is naturally steerable. Complete steerability, though, is achieved by utilizing the Fourier-Argand representation, which provides a steerable filter able to estimate the amplitude and direction of image features, even in the presence of very high noise. We demonstrate the efficiency of the representation by comparing how it performs in wavelet-based denoising algorithms.