scholarly journals Image Deblurring under Impulse Noise via Total Generalized Variation and Non-Convex Shrinkage

Algorithms ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 221
Author(s):  
Lin ◽  
Chen ◽  
Chen ◽  
Yu
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Signal To Noise Ratio ◽  
Image Deblurring ◽  
L1 Norm ◽  
Signal To Noise ◽  
Total Generalized Variation ◽  
First Order ◽  
Norm Constraint ◽  
Generalized Variation

Image deblurring under the background of impulse noise is a typically ill-posed inverse problem which attracted great attention in the fields of image processing and computer vision. The fast total variation deconvolution (FTVd) algorithm proved to be an effective way to solve this problem. However, it only considers sparsity of the first-order total variation, resulting in staircase artefacts. The L1 norm is adopted in the FTVd model to depict the sparsity of the impulse noise, while the L1 norm has limited capacity of depicting it. To overcome this limitation, we present a new algorithm based on the Lp-pseudo-norm and total generalized variation (TGV) regularization. The TGV regularization puts sparse constraints on both the first-order and second-order gradients of the image, effectively preserving the image edge while relieving undesirable artefacts. The Lp-pseudo-norm constraint is employed to replace the L1 norm constraint to depict the sparsity of the impulse noise more precisely. The alternating direction method of multipliers is adopted to solve the proposed model. In the numerical experiments, the proposed algorithm is compared with some state-of-the-art algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), signal-to-noise ratio (SNR), operation time, and visual effects to verify its superiority.

scholarly journals Artefact Removal from EEG Signals using Total Variation De-noising

2020 ◽  
Vol 9 (5) ◽  
pp. 2357-2361
Keyword(s):  
Root Mean Square Error ◽  
Total Variation ◽  
Signal To Noise Ratio ◽  
Mean Square ◽  
Health Issues ◽  
Eeg Signals ◽  
Signal To Noise ◽  
Medical Practitioners ◽  
Artefact Removal ◽  
Two Parameters

Artefacts removing (de-noising) from EEG signals has been an important aspect for medical practitioners for diagnosis of health issues related to brain. Several methods have been used in last few decades. Wavelet and total variation based de-noising have attracted the attention of engineers and scientists due to their de-noising efficiency. In this article, EEG signals have been de-noised using total variation based method and results obtained have been compared with the results obtained from the celebrated wavelet based methods . The performance of methods is measured using two parameters: signal-to-noise ratio and root mean square error. It has been observed that total variation based de-noising methods produce better results than the wavelet based methods.

scholarly journals Performance of relaxed iterative methods for image deblurring problems

2019 ◽  
Vol 13 ◽  
pp. 174830261986173 ◽  
Author(s):  
Jae H Yun
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Total Variation ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Image Deblurring ◽  
Total Variation Regularization ◽  
L1 Norm ◽  
Split Bregman ◽  
Relaxation Parameters

In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods.

scholarly journals Simultaneous Determination of Dapsone and Pyrimethamine by Derivative Spectrophotometry in Pharmaceutical Formulations

2003 ◽  
Vol 86 (2) ◽  
pp. 241-245 ◽  
Author(s):  
M Inés Toral ◽  
Andrés Tassara ◽  
César Soto ◽  
Pablo Richter
Keyword(s):  
Simultaneous Determination ◽  
Signal To Noise Ratio ◽  
Pharmaceutical Formulations ◽  
Derivative Spectrophotometry ◽  
Fast Method ◽  
Signal To Noise ◽  
Zero Crossing ◽  
First Order ◽  
First Derivative

Abstract A simple and fast method was developed for the simultaneous determination of dapsone and pyrimethamine by first-order digital derivative spectrophotometry. Acetonitrile was used as a solvent to extract the drugs from the pharmaceutical formulations, and the samples were subsequently evaluated directly by digital derivative spectrophotometry. The simultaneous determination of both drugs was performed by the zero-crossing method at 249.4 and 231.4 nm for dapsone and pyrimethamine, respectively. The best signal-to-noise ratio was obtained when the first derivative of the spectrum was used. The linear range of determination for the drugs was from 6.6 × 10−7 to 2.0 × 10−4 and from 2.5 × 10−6 to 2.0 × 10−4 mol/L for dapsone and pyrimethamine, respectively. The excipients of commercial pharmaceutical formulations did not interfere in the analysis. Chemical and spectral variables were optimized for determination of both analytes. A good level of repeatability, 0.6 and 1.7% for dapsone and pyrimethamine, respectively, was observed. The proposed method was applied for the simultaneous determination of both drugs in pharmaceutical formulations.

scholarly journals Infrared Image Deblurring via High-Order Total Variation and Lp-Pseudonorm Shrinkage

2020 ◽  
Vol 10 (7) ◽  
pp. 2533 ◽  
Author(s):  
Jingjing Yang ◽  
Yingpin Chen ◽  
Zhifeng Chen
Keyword(s):  
Total Variation ◽  
Infrared Image ◽  
Noise Pollution ◽  
Image Deblurring ◽  
High Order ◽  
L1 Norm ◽  
Alternating Direction ◽  
Image Blurring ◽  
Image Gradients ◽  
Staircase Artifacts

The quality of infrared images is affected by various degradation factors, such as image blurring and noise pollution. Anisotropic total variation (ATV) has been shown to be a good regularization approach for image deblurring. However, there are two main drawbacks in ATV. First, the conventional ATV regularization just considers the sparsity of the first-order image gradients, thus leading to staircase artifacts. Second, it employs the L1-norm to describe the sparsity of image gradients, while the L1-norm has a limited capacity of depicting the sparsity of sparse variables. To address these limitations of ATV, a high-order total variation is introduced in the ATV deblurring model and the Lp-pseudonorm is adopted to depict the sparsity of low- and high-order total variation. In this way, the recovered image can fit the image priors with clear edges and eliminate the staircase artifacts of the ATV model. The alternating direction method of multipliers is used to solve the proposed model. The experimental results demonstrate that the proposed method does not only remove blurs effectively but is also highly competitive against the state-of-the-art methods, both qualitatively and quantitatively.

Adaptive Kalman Filtering: A Simulation Result

1988 ◽  
Vol 110 (1) ◽  
pp. 104-107 ◽  
Author(s):  
J. Z. Sasiadek ◽  
P. J. Wojcik
Keyword(s):  
Kalman Filtering ◽  
Design Methodology ◽  
Signal To Noise Ratio ◽  
Performance Tests ◽  
Signal To Noise ◽  
First Order ◽  
Order Spectrum ◽  
On Line ◽  
Sensor Signals ◽  
Unknown Signal

This paper presents the algorithm for on-line adaptive Kalman filtering of sensor signals with unknown signal to noise ratio. A first order spectrum of a pure signal and white Gaussian measurement noise have been assumed. The results of the performance tests of the algorithm as well as the design methodology of the adaptive filter are given.

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