Design of oversampled cosine-sine modulated filter banks for directional image representation

We propose an oversampled cosine-sine modulated filter bank (OCSMFB) for richer overcompleteness contributing sparse directional image representation. The CSMFB, proposed as an alternative of the dual-tree complex wavelet transform (DTCWT), can be designed easily by modulating a prototype filter and can work in image processing tasks better than the DTCWT. However, the conventional CSMFB consists of two critically-sampled FB, and its non-redundancy restricts design degree of freedom and overcomplete image representation. This paper relaxes the redundancy of the conventional CSMFB by oversampling each CMFB and SMFB. For design of the OC-SMFB, we present the perfect reconstruction (PR) condition and the parameterization, in order to satisfy the PR structurally. Moreover, the parameterization for structural regularity, which provides NO DC leakage, is discussed. The experimental results of image denoising show the OCSMFB can work better than the CSMFB.