Hybrid inter- and intra-wavelet scale image restoration

This paper exploits both the interand intra-scale interdependencies that exist in wavelet coe3cients to improve image restoration from noise-corrupted data. Using an over-complete wavelet expansion, we group the wavelet coe3cients with the same spatial orientation at several scales. We then apply the linear minimum mean squared-error estimation to smooth noise. This scheme exploits the inter-scale correlation information of wavelet coe3cients. To exploit the intra-scale dependencies, we calculate the co-variance matrix of each vector locally using a centered square-shaped window. Experiments show that the proposed hybrid scheme signi7cantly outperforms methods exploiting only the intraor inter-scale dependencies. The performance of noise removal also depends on wavelet 7lters. In our experiments a biorthogonal wavelet, which best characterizes the image inter-scale dependencies, achieves the best results. ? 2003 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.