Removing the geometric distortion and space-time-varying blur caused by atmospheric turbulence from a given image sequence remains a challenge. Since geometric distortion and blur are two different kinds of distortions and interact with each other in the process of image restoration, it is difficult to extract the features that are useful to the restoration process when the images experience multiple distortions. In this article, we propose a new scheme based on geometric distortion and blur representation. The blur invariants and maximum gradient are used to represent the geometric distortion and sharpness of an image frame, respectively. The proposed scheme consists of three parts. First, two fast frame selection algorithms based on independent evaluations of the sharpness and geometric distortion are proposed to subsample a sharp subsequence and obtain a reference image. Next, to suppress the geometric distortion, a moment-blur-invariant-based method is presented to estimate the deformation vector between two degraded frames, and the selected sharp frames are registered to the reference image. Finally, a blind deconvolution method is applied to deblur the fused image, generating a final restoration result. Various experimental results show that the proposed method can effectively alleviate distortion and blur, as well as significantly improve the visual quality of real atmospheric turbulence-degraded images.

This paper presents a novel fast algorithm for digital convolutions. It is able to compute arbitrary-length convolutions more efficiently via transforming the convolution into a first-order moment. Although many additions are required, the proposed algorithm has some advantages such as the avoidance of multiplications, simple computation structure, and only integer additions. These advantages contribute to this algorithm being so easy that it can compute convolutions rapidly. Based on the proposed algorithm a very simple and scalable systolic array without multipliers and ROM has been developed leading to more efficient VLSI implementation of convolutions.

Geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning. In this brief, the notion of scaled convex hull (SCH) is defined and a set of theoretical results are exploited to support it. These results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently. Then, the popular S-K algorithm has been presented to solve the nonseparable problems in the context of the SCH framework. The theoretical analysis and some experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the number of kernel evaluations and the execution time.