基于双树小波通用隐马尔可夫树模型的图像压缩感知

练秋生; 王艳

doi:10.3724/SP.J.1146.2009.01153

基于双树小波通用隐马尔可夫树模型的图像压缩感知

doi: 10.3724/SP.J.1146.2009.01153

练秋生,
王艳

基金项目:

国家自然科学基金(60772079)和河北省自然科学基金(F2010001294)资助课题

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出版历程
- 收稿日期: 2009-09-01
- 修回日期: 2010-05-13
- 刊出日期: 2010-10-19

Image Compressed Sensing Based on Universal HMT of the Dual-tree Wavelets

摘要

摘要: 标准压缩感知图像重构仅利用图像小波系数具有稀疏性的先验知识，未能利用小波系数的结构分布特性。利用基于模型压缩感知重构思想，将能有效描述图像小波系数分布特性的隐马尔可夫树(HMT)模型引入到图像的压缩感知重构。经过理论推导，将基于HMT模型的重构转化为型如标准图像压缩感知重构的优化问题，并提出基于贝叶斯优化的凸集交替投影法进行求解。为进一步提高重构质量和速度，引入了双树小波域通用HMT (uHMT)模型及改进的uHMT (iuHMT)模型代替小波域HMT模型。实验结果表明，基于双树小波域iuHMT模型的重构图像的平均峰值信噪比(PSNR)比uHMT模型高0.97 dB.
- 压缩感知 /
- 模型压缩感知 /
- 双树小波 /
- uHMT模型 /
- 凸集交替投影
Abstract: The standard Compressed Sensing (CS) reconstructions of image exploit simply the sparse priors of the wavelet coefficients, ignoring the structural information of the wavelet coefficients. In this paper, the Hidden Markov Tree ( HMT ) model is integrated in the compressed sensing，which has been found successful in capturing the key features of the joint probability density of the wavelet coefficients of real-world image. An optimization issue which is similar to the standard compressed sensing is derived from the MAP reconstructions for the image based on HMT model, and an alternating convex projection algorithm based on Bayesian optimization is proposed. Whats more, a universal HMT (uHMT) model based on the dual-tree wavelet transform and its improved form are integrated to improve the reconstruction performance further, instead of the HMT model of the orthogonal wavelet transform. As the experiments show, the average Peak Signal-to-Noise Ratio (PSNR) of the reconstructed image based on the improved uHMT (iuHMT) model in the dual-tree wavelets domain outperforms uHMT model 0.97 dB.
- Compressed Sensing (CS) /
- Model-based CS /
- Dual-tree wavelet /
- uHMT model /
- Alternating convex projection

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