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2. The upper bound of phase transition point of multi literal satisfiability problem.

Author

LU Lei, WANG Xiao-feng, LIANG Chen, and ZHANG Jiu-long

Abstract

The satisfiability problem (SAT) refers to whether there is a set of boolean variable assignments that make at least one literal in each clause of the conjunctive normal form (CNF) formula true. The multi literal SAT problem refers to whether there is a set of boolean variable assignments that make at least two literals in each clause of the CNF formula true. Obviously, this problem is still an NP difficult problem. Defining as the ratio of the number of clauses in the CNF formula to the number of variables, we study the upper bound α* of phase transition point of the problem. If α strictly exceeds α*, the multi literal satisfaction problem is almost certainly unsatisfiable. A simple inference of the first moment can be used to prove α* =-ln 2/ln1-(k+1)/2k). α* =1 when k=3. The local maximum technique proposed by Kirousis et al is used to improve the upper bound α* of phase transition point of the multi literal 3-SAT problem to 0.719 3. Finally, a large amount of data is selected for experimental verification, and the results show that the theoretical results are consistent with the experimental results [ABSTRACT FROM AUTHOR]

Published
2022
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4. SAR Image Processing Based on Fast Discrete Curvelet Transform

Author

Zhang Jiu-long, Zhang Xiaodan, and Zhang Zhiyu

Subjects
Synthetic aperture radar, Computer science, business.industry, Wavelet transform, Speckle noise, Pattern recognition, Image processing, Mathematics::Numerical Analysis, Speckle pattern, Wavelet, Computer Science::Computer Vision and Pattern Recognition, Radar imaging, Curvelet, Computer vision, Artificial intelligence, business
Abstract

Curvelet transform is a new kind of multiscale analysis algorithm which is more suitable for image processing, as compared with Wavelet it can better analysis the line and curve edge characteristics, and it has better approximation precision and sparsity description, also has good directivity. This paper introduces that remote sensing image speckle reduction based on Curvelet transform. Synthetic Aperture Radar (SAR) image is easily polluted by speckle noise, which can affect further processing of SAR image. This paper put forward method of SAR image speckle deduction based on Fast Discrete Curvelet Transform (FDCT). This method firstly transform SAR image to Curvelet domain by using FDCT, and get the Curvelet coefficient, then estimate the Curvelet coefficient threshold of different scale and direction by using adaptive threshold method, treatment on Curvelet coefficient with hard threshold and soft threshold respectively, and the last recovery the original image by using IFDCT. This paper uses this method to single-look SAR image and compare with Wavelet de-noising method, the result shows that the effect of Curvelet flitting is better than Wavelet flitting, and the soft threshold is better than hard threshold.

Published
2009

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