No abstract

In recent years, due to its anisotropy, multi-directional capture characteristics, and translation invariance, the non-subsampled shearlet transform (NSST) has played an important stabilizing role in the process of image restoration. In this study, we analyze an image's NSST coefficients, including the relationship between coefficients in the same subband, the relationship between "father-son" coefficients, and the relationship between "brotherhood" coefficients in different subbands. The results reveal that the coefficients in the NSST subbands are sparse, and both "father-son relationship" and "brotherhood relationship" coefficients exhibit aggregation and transitivity. On this basis, a hidden Markov tree (HMT) model with associated multi-state coefficients (M-NSST-HMT) is proposed. This model estimates the reconstructed coefficients using "father-son relationship" and "brotherhood relationship" of the NSST subband coefficients as joint states of guiding the coefficients' transfer between subbands. In addition, the model integrates the reconstructed coefficients using the mutual information between these two associated states. Finally, the proposed model is applied to image denoising with favorable results. The results indicate that the proposed model can reveal the relationship of coefficients in NSST subbands and improve the prediction accuracy of coefficients more effectively than the traditional HMT model.