On The Design Of Non-aliasing Contourlet Filter Banks And Its Application In CS-MRI

The Contourlet transform is regarded as a"real"image representation. It is constructed by combining directional filter banks (DFBs) and Laplacian pyramid (LP). The shape of Contourlet basis in frequency domain is like a contour segment, which makes it more efficient to represent natural images than wavelet transform. However, the real Contourlet basis do not localized in frequency domain, there are some undesired components, which limit the application effect of Contourlet transform. We regard this as the aliasing phenomenon of Contourlet transform. This thesis studies the non-aliasing Contourlet transform.Firstly, we study the reason of the aliasing of Contourlet basis in frequency domain. The directional subbands of DFB in practice are of non-ideal situation, and the combination of LP structure makes the transition band of DFB spread to unexpected domain. By a graphic and mathematical analysis of this procedure, we point out that the main reason of aliasing is the downsampling operation in LP structure.Secondly, we research two different methods of constructing non-aliasing Contourlet transform, and give some advanced design of each method. The first method is to constrain the stopband frequency response of lowpass filters in LP structure, which can effectively cancel the aliasing. The second method is based on a two channel filter bank based multiresolution structure. To realize this structure, we study two design methods of this multiresolution structure, including time domain based and frequency domain based design.Finally, we apply the non-aliasing Contourlet transform to compressed-sensing (CS) based MR imaging (CS-MRI) reconstruction. CS has emerged as a theoretical foundation for reconstruction of MR images, which can highly reduce the acquisition time of MRI. Since the wavelet transform for CS-MRI does not sparely represent curves and edges, the non-aliasing Contourlet transform outperforms traditional Contourlet in representation ability. We introduce non-aliasing Contourlet transform for CS-MRI reconstruction. Simulation results demonstrate that the non-aliasing based CS-MRI can better reconstruct the MR images than wavelet and aliasing Contourlet transforms.