Non-Parametric Bayesian Dictionary Learning for Sparse Image Representations
Non-Parametric Bayesian Dictionary Learning for Sparse Image Representations
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发表时间：
2009-12
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通讯作者：
Mingyuan Zhou;Haojun Chen;J. Paisley;Lu Ren;G. Sapiro;L. Carin
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作者：
Mingyuan Zhou;Haojun Chen;J. Paisley;Lu Ren;G. Sapiro;L. Carin
非参数贝叶斯技术被考虑用于学习稀疏图像表示的字典，应用于去噪、图像修复和压缩感知（CS）。β过程被用作学习字典的先验，并且这种非参数方法自然地推断出合适的字典大小。狄利克雷过程和概率截棍过程也被考虑用于挖掘图像内的结构。所提出的方法可以原位学习稀疏字典；如果有训练图像则可以利用，但并非必需。此外，噪声方差不需要已知，并且可以是非平稳的。所提出方法的另一个优点是可以容易地采用序贯推理，从而允许扩展到大型图像。给出了几个示例结果，同时使用了吉布斯和变分贝叶斯推理，并与其他最先进的方法进行了比较。
Non-parametric Bayesian techniques are considered for learning dictionaries for sparse image representations, with applications in denoising, inpainting and compressive sensing (CS). The beta process is employed as a prior for learning the dictionary, and this non-parametric method naturally infers an appropriate dictionary size. The Dirichlet process and a probit stick-breaking process are also considered to exploit structure within an image. The proposed method can learn a sparse dictionary in situ; training images may be exploited if available, but they are not required. Further, the noise variance need not be known, and can be non-stationary. Another virtue of the proposed method is that sequential inference can be readily employed, thereby allowing scaling to large images. Several example results are presented, using both Gibbs and variational Bayesian inference, with comparisons to other state-of-the-art approaches.