Piecewise smoothness of conjugate homeomorphisms of a circle with corners

1999 ◽  
Vol 120 (2) ◽  
pp. 961-972 ◽  
Author(s):  
A. A. Dzhalilov
Keyword(s):  
Piecewise Smoothness

scholarly journals Cell-filtering-based multi-scale Shannon–Cosine wavelet denoising method for locust slice images

2019 ◽  
Vol 17 (05) ◽  
pp. 1950035 ◽  
Author(s):  
Shenghan Mei ◽  
Xiaochun Liu ◽  
Shuli Mei
Keyword(s):  
Signal To Noise Ratio ◽  
Gaussian White Noise ◽  
Similarity Index ◽  
Structural Similarity ◽  
Wavelet Denoising ◽  
Experimental Results ◽  
Transform Method ◽  
Denoising Method ◽  
Multi Scale ◽  
Piecewise Smoothness

The locust slice images have all the features such as strong self-similarity, piecewise smoothness and nonlinear texture structure. Multi-scale interpolation operator is an effective tool to describe such structures, but it cannot overcome the influence of noise on images. Therefore, this research designed the Shannon–Cosine wavelet which possesses all the excellent properties such as interpolation, smoothness, compact support and normalization, then constructing multi-scale wavelet interpolative operator, the operator can be applied to decompose and reconstruct the images adaptively. Combining the operator with the local filter operator (mean and median), a multi-scale Shannon–Cosine wavelet denoising algorithm based on cell filtering is constructed in this research. The algorithm overcomes the disadvantages of multi-scale interpolation wavelet, which is only suitable for describing smooth signals, and realizes multi-scale noise reduction of locust slice images. The experimental results show that the proposed method can keep all kinds of texture structures in the slice image of locust. In the experiments, the locust slice images with mixture noise of Gaussian and salt–pepper are taken as examples to compare the performances of the proposed method and other typical denoising methods. The experimental results show that the Peak Signal-To-Noise Ratio (PSNR) of the denoised images obtained by the proposed method is greater 27.3%, 24.6%, 2.94%, 22.9% than Weiner filter, wavelet transform method, median and average filtering, respectively; and the Structural Similarity Index (SSIM) for measuring image quality is greater 31.1%, 31.3%, 15.5%, 10.2% than other four methods, respectively. As the variance of Gaussian white noise increases from 0.02 to 0.1, the values of PSNR and SSIM obtained by the proposed method only decrease by 11.94% and 13.33%, respectively, which are much less than other 4 methods. This shows that the proposed method possesses stronger adaptability.

scholarly journals Application of spatially related MRF model in NMF hyperspectral unmixing

2018 ◽  
Vol 232 ◽  
pp. 02003
Author(s):  
Bo Yuan
Keyword(s):  
Spatial Correlation ◽  
Hyperspectral Image ◽  
Signal Identification ◽  
Hyperspectral Unmixing ◽  
Spatial Distribution Characteristics ◽  
Linear Unmixing ◽  
Piecewise Smoothness ◽  
Vertex Component Analysis ◽  
Fully Constrained Least Squares ◽  
Non Negative Matrix Factorization

Aiming at Non-negative Matrix Factorization (NMF)’s problem of initialization and "local minima" in hyperspectral unmixing, a NMF linear unmixing algorithm with spatial correlation constrains (SCNMF) based on Markov Random Field (MRF) was proposed. Firstly, Hyperspectral Signal identification by minimum error (HySime) method was adopted to estimate the number of endmembers, initialized endmember matrix and abundance matrix by Vertex Component Analysis (VCA) and Fully Constrained Least Squares (FCLS) respectively. then established energy function to depict the spatial distribution characteristics of ground objects by MRF model. Finally, spatial correlation constraint based on MRF model and NMF standard objective function were combined in the form of altemating iteration to estimate endmember spectrum and abundance of hyperspectral image. Theoretical analysis and experimental results indicated that, the endmember decomposition precision of SCNMF is 10.6% higher than that of Minimum Volume Constrained NMF (MVC-NMF), 12.3% higher than that of Piecewise Smoothness NMF with Sparseness Constraints(PSNMFSC), 14.1% higher than that of NMF with Alternating Projected Subgradients(APS-NMF); the abundance decomposition precision of SCNMF is 14.4% higher than that of MVC-NMF, 15.9% higher than that of PSNMFSC, 15.3% higher than that of APS-NMF.The proposed SCNMF can remedy NMF's deficiency in describing spatial correlation characteristics, and decrease spatial energy distribution error.

scholarly journals Spatial and temporal regularization to estimate COVID-19 reproduction number R(t): Promoting piecewise smoothness via convex optimization

PLoS ONE ◽  
2020 ◽  
Vol 15 (8) ◽  
pp. e0237901 ◽  
Author(s):  
Patrice Abry ◽  
Nelly Pustelnik ◽  
Stéphane Roux ◽  
Pablo Jensen ◽  
Patrick Flandrin ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Reproduction Number ◽  
Piecewise Smoothness
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