Two-dimensional FIR notch filter design using singular value decomposition

1998 ◽  
Vol 45 (3) ◽  
pp. 290-294 ◽  
Author(s):  
S.-C. Fei ◽  
W.-S. Lu ◽  
C.-C. Tseng
Keyword(s):  
Singular Value Decomposition ◽  
Filter Design ◽  
Notch Filter ◽  
Singular Value ◽  
Two Dimensional ◽  
Value Decomposition

scholarly journals Dual Zero-Watermarking Scheme for Two-Dimensional Vector Map Based on Delaunay Triangle Mesh and Singular Value Decomposition

2019 ◽  
Vol 9 (4) ◽  
pp. 642 ◽  
Author(s):  
Xu Xi ◽  
Xinchang Zhang ◽  
Weidong Liang ◽  
Qinchuan Xin ◽  
Pengcheng Zhang
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Two Dimensional ◽  
Triangle Mesh ◽  
Vector Map ◽  
Vector Maps ◽  
Feature Sequence ◽  
Zero Watermarking ◽  
Value Decomposition ◽  
Watermarking Scheme

Digital watermarking is important for the copyright protection of electronic data, but embedding watermarks into vector maps could easily lead to changes in map precision. Zero-watermarking, a method that does not embed watermarks into maps, could avoid altering vector maps but often lack of robustness. This study proposes a dual zero-watermarking scheme that improves watermark robustness for two-dimensional (2D) vector maps. The proposed scheme first extracts the feature vertices and non-feature vertices of the vector map with the Douglas-Peucker algorithm and subsequently constructs the Delaunay Triangulation Mesh (DTM) to form a topological feature sequence of feature vertices as well as the Singular Value Decomposition (SVD) matrix to form intrinsic feature sequence of non-feature vertices. Next, zero-watermarks are obtained by executing exclusive disjunction (XOR) with the encrypted watermark image under the Arnold scramble algorithm. The experimental results show that the scheme that synthesizes both the feature and non-feature information improves the watermark capacity. Making use of complementary information between feature and non-feature vertices considerably improves the overall robustness of the watermarking scheme. The proposed dual zero-watermarking scheme combines the advantages of individual watermarking schemes and is robust against such attacks as geometric attacks, vertex attacks and object attacks.

Enhancement of 3D GPR datasets using singular value decomposition applied in 2D the spectral domain for clutter noise removal

2021 ◽  
Author(s):  
Rui Jorge Oliveira ◽  
Bento Caldeira ◽  
Teresa Teixidó ◽  
José Fernando Borges
Keyword(s):  
Singular Value Decomposition ◽  
Filter Design ◽  
Archaeological Site ◽  
Noise Removal ◽  
Computational Effort ◽  
Singular Value ◽  
Spectral Domain ◽  
Buried Structures ◽  
3D Gpr ◽  
Value Decomposition

<p>The ground-penetrating radar (GPR) datasets obtained in archaeological environments have substantial problems related the presence of clutter noise. These noisy reflections are generated by the heterogeneities of the ground and by the collapses of structures buried in the ground, that can prevent a good assessment of the subsurface with this method. The classic filtering operations available can fail to remove it effectively. This work presents an approach to filtering the GPR data in the 2D spectral domain through the singular value decomposition (SVD) factorization technique. The spectral domain present advantages such as the circular symmetry of the transformed data that turns easy the filter parametrisation and the constant computational effort whatever the amount of data considered. SVD allows the decreasing of the user dependency to parametrize the filter. The main propose of this method is to classify automatically the datasets into useful information, corresponding to buried structures, and noise, to remove the last. This approach was conceived based on the study of the GPR signal in the 2D spectral domain and the manual filter design. The tests were performed with different datasets, one from a laboratory experiment (controlled environment) and the other from a field acquisition in an archaeological site (uncontrolled environment) with subsequent excavation to proof the results. The proposed approach is effective to remove the clutter noise in the GPR datasets and constitutes a complementary operation to those already existing in the commercial software.</p><p> </p><p>Acknowledgment: The work was supported by the Portuguese Foundation for Science and Technology (FCT) project UIDB/04683/2020 - ICT (Institute of Earth Sciences) and by the INTERREG 2014-2020 Program, through the "Innovación abierta e inteligente en la EUROACE" Project, with the reference 0049_INNOACE_4_E.</p>

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