CIF:SMALL: Image Restoration via Bayesian Structured Sparse Coding

图像质量下降是不可避免的，在各种科学和工程应用，如生物医学/天文成像和易出错的图像通信。基于物理的解决方案来对抗这些不利因素（例如，传感器噪声、光学模糊和信道误差）通常太昂贵;因此，非常希望开发计算备选方案来挽救那些退化的图像。计算效率和高质量的图像恢复算法可以找到从节能传感到更实惠的医疗保健的广泛应用。首先是以原则性的方式描述图像的非局部不变性和局部变化。将开发一种称为贝叶斯结构化稀疏编码的新框架，以统一和扩展现有的几类模型（例如，基于小波的和基于块的）用于自然图像。第二，新的理论框架将有利于发明计算效率高的推理算法的图像恢复应用。沿着这条研究路线的最终目标是使贝叶斯图像恢复算法不仅在理论上是最优的，而且在实践中是可行的。

Image quality degradation is inevitable in various scientific and engineering applications such as biomedical/astronomical imaging and error-prone image communications. Physics-based solutions to fight against those adversary factors (e.g., sensor noise, optical blur and channel errors) are often too expensive; therefore it is highly desirable to develop computational alternatives to salvage those degraded images. Computationally efficient and high-quality image restoration algorithms could find a wide range of applications from energy-efficient sensing to more-affordable healthcare.This research contains two components. First is to characterize both nonlocal invariance and local variation of images in a principled fashion. A new framework called Bayesian structured sparse coding will be developed to unify and extend several existing classes of models (e.g., wavelet-based and patch-based) for natural images. Second, the new theoretical framework will facilitate the invention of computationally efficient inference algorithms for image restoration applications. The ultimate objective along this line of research is to make the developed Bayesian image restoration algorithms not only theoretically optimal but also practically feasible.