scholarly journals The Sylvester Resultant Matrix and Image Deblurring

Author(s):  
Joab R. Winkler
2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.


2013 ◽  
Vol 24 (5) ◽  
pp. 1143-1154 ◽  
Author(s):  
Shu TANG ◽  
Wei-Guo GONG ◽  
Jian-Hua ZHONG

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5312
Author(s):  
Yanni Zhang ◽  
Yiming Liu ◽  
Qiang Li ◽  
Jianzhong Wang ◽  
Miao Qi ◽  
...  

Recently, deep learning-based image deblurring and deraining have been well developed. However, most of these methods fail to distill the useful features. What is more, exploiting the detailed image features in a deep learning framework always requires a mass of parameters, which inevitably makes the network suffer from a high computational burden. We propose a lightweight fusion distillation network (LFDN) for image deblurring and deraining to solve the above problems. The proposed LFDN is designed as an encoder–decoder architecture. In the encoding stage, the image feature is reduced to various small-scale spaces for multi-scale information extraction and fusion without much information loss. Then, a feature distillation normalization block is designed at the beginning of the decoding stage, which enables the network to distill and screen valuable channel information of feature maps continuously. Besides, an information fusion strategy between distillation modules and feature channels is also carried out by the attention mechanism. By fusing different information in the proposed approach, our network can achieve state-of-the-art image deblurring and deraining results with a smaller number of parameters and outperform the existing methods in model complexity.


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