系数多状态关联的图像NSST-HMT模型

Image NSST-HMT model with associated multi-state coefficients

近年来,非下采样Shearlet变换(non-subsampled shearlet transform, NSST)因其具有各向异性,多方向捕捉性的同时,还兼具平移不变性,从而在图像恢复过程中发挥着重要的稳定作用.本文首先对图像NSST子带内系数关系、子带间系数的'父子关系'和'兄弟关系' 3方面进行分析,获得子带内系数具有稀疏性、子带间'父子关系'和'兄弟关系'系数均具有聚集性和传递性的结论.在此基础上提出一种基于系数多状态关联的隐Markov树模型(multi-state non-subsampled shearlet transform hidden Markov tree, M-NSST-HMT),该模型通过将NSST子带间系数的'父子关系'和'兄弟关系'作为共同指导子带间系数传递的状态来估计重构系数,并利用两种状态关联的互信息来对重构系数进行整合.最后将所提出的模型应用于图像去噪并取得良好的去噪效果,结果表明所提出的模型较传统HMT模型能够更好地揭示图像NSST变换后子带内和子带间系数的关系,并提高系数的预测准确性.

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(MNSST-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.