Multiscale LMMSE-based image denoising with optimal wavelet selection

In this paper, a wavelet-based multiscale linear minimum mean square-error estimation (LMMSE) scheme for image denoising is proposed, and the determination of the optimal wavelet basis with respect to the proposed scheme is also discussed. The overcomplete wavelet expansion (OWE), which is more effective than the orthogonal wavelet transform (OWT) in noise reduction, is used. To explore the strong interscale dependencies of OWE, we combine the pixels at the same spatial location across scales as a vector and apply LMMSE to the vector. Compared with the LMMSE within each scale, the interscale model exploits the dependency information distributed at adjacent scales. The performance of the proposed scheme is dependent on the selection of the wavelet bases. Two criteria, the signal information extraction criterion and the distribution error criterion, are proposed to measure the denoising performance. The optimal wavelet that achieves the best tradeoff between the two criteria can be determined from a library of wavelet bases. To estimate the wavelet coefficient statistics precisely and adaptively, we classify the wavelet coefficients into different clusters by context modeling, which exploits the wavelet intrascale dependency and yields a local discrimination of images. Experiments show that the proposed scheme outperforms some existing denoising methods.