A nonconvex [Formula: see text] regularization model and the ADMM based algorithm
Zhuang Fang1, Tang Liming1, Wu Liang1
1School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000 People's Republic of China.
Scientific Reports
|May 13, 2022
Summary
This study introduces a new nonconvex regularization model for image restoration, significantly improving edge preservation in salt and pepper noise removal. The proposed method enhances image quality and detail compared to traditional techniques.
Area of Science:
- Image processing
- Computer vision
- Applied mathematics
Background:
- Traditional total variation (TV) regularization struggles with edge preservation in salt and pepper noise removal.
- Existing methods often compromise image details during noise reduction.
Purpose of the Study:
- To develop a novel nonconvex regularization model for enhanced image restoration.
- To improve edge and contour preservation during salt and pepper noise removal.
Main Methods:
- Proposed a nonconvex [Formula: see text]-norm regularizer in the total variation domain.
- Utilized [Formula: see text] fidelity for noise measurement.
- Employed an alternating direction method of multipliers (ADMM) with majorization-minimization (MM) and proximity operators for solving the model.
Main Results:
- The proposed model effectively removes salt and pepper noise while preserving image edges and contours.
- Achieved superior performance over state-of-the-art variational regularization models.
- Demonstrated approximately 0.5 dB PSNR and 0.06 MSSIM improvements.
Conclusions:
- The nonconvex [Formula: see text] regularization model offers superior edge-preserving capabilities for image restoration.
- The developed ADMM-based algorithm provides an effective and convergent solution.
- This approach represents a significant advancement in noise reduction and image detail preservation.
Related Concept Videos
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
107
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
107
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
763
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
763
01:11Residuals and Least-Squares Property
7.9K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
7.9K
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
130
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
130
01:06Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
132
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
132
01:17Clearance Models: Noncompartmental Models
106
Clearance is a pharmacokinetic parameter traditionally defined by compartment models, signifying the rate at which a drug is expelled from the body. However, a noncompartmental model offers an alternative method for assessing clearance, primarily employing empirical data obtained after administering a single drug dose.
The noncompartmental approach capitalizes on extensive sampling data, correlating the volume of distribution to systemic exposure and the administered dosage. This method enables...
The noncompartmental approach capitalizes on extensive sampling data, correlating the volume of distribution to systemic exposure and the administered dosage. This method enables...
106