A Nonconvex Model with Minimax Concave Penalty for Image Restoration

You, Juntao; Jiao, Yuling; Lu, Xiliang; Zeng, Tieyong

doi:10.1007/s10915-018-0801-z

Cited by 43 publications

(21 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In building ensemble forecasting model, five penalized regressions that consist of Ridge, Lasso, Elastic Net, SCAD, and MCP will be trained and validated by each. Ridge regression widely used for high dimensional data where independendent variables are highly correlated, this method aims to reduce multicollinearity [13], Lasso is a method that used regularization and variable selection to increase interpretability and accuracy [14], Elastic Net is a combination of Ridge and Lasso regressions, so it will retain the advantage of both methods [15], SCAD regression aims to improve Lasso's penalty by reducing the bias in the model because the Lasso penalty tends to be linear in the size of the regression coefficient [16], and MCP is other alternative to give less biased variables in sparse model [17]. Penalized regression parameter will be determined.…”

Section: Methodsmentioning

confidence: 99%

Forecasting the number of dengue fever based on weather conditions using ensemble forecasting method

Nabilah

Tyasnurita²,

Mahananto³

et al. 2023

IJ-AI

View full text Add to dashboard Cite

<p><span lang="EN-US">Dengue fever is still a crucial public health problem in Indonesia, with the highest fatality rate (CFR) is 1.01% in East Java, Malang Regency. One of the solutions to control the death rate and cases is to forecast the cases number. This study proposed ensemble forecasting that build from several penalized regressions. Penalized regressions are able to overcome linear regression analysis’ shortcomings by using penalty values, that will affect regression’s coefficient, resulting on regression model with a slight bias in order to reduce parameter estimations and prediction values' variances. Penalized regressions are evaluated and built as ensemble forecasting method to minimize the shortcomings of other existing model, so it could produce more accurate values comparing to single penalized regression model. The result showed that the ensemble model `consists of smoothly clipped absolute deviation (SCAD) and Elastic-net is sufficient to capture data patterns with root mean squared error (RMSE) 6.38. </span></p>

show abstract

Section: Methodsmentioning

confidence: 99%

Forecasting the number of dengue fever based on weather conditions using ensemble forecasting method

Nabilah

Tyasnurita²,

Mahananto³

et al. 2023

IJ-AI

View full text Add to dashboard Cite

show abstract

“…To promote sparsity of the target signals and images, recent studies show that nonconvex approximations of the l 0 -norm are more efficient, and the nonconvex penalties usually have better performances than l 1 penalty [1,2]. This is because the l 1 regularized model induces bias for large coefficients [3].…”

Section: Comparsion Between L 0 and L 1 Normmentioning

confidence: 99%

The first direct method of spot sparsity optimization for proton arc therapy

Zhao¹,

You

Liu

et al. 2023

Acta Oncologica

View full text Add to dashboard Cite

Notations and outlineWe describe the notation that we will use throughout the paper. We use regular lowercase letters for scalars, bold lowercase letters for vectors, BOLD CAPITAL LETTERS for matrices, and normal CAPITAL LETTERS for sets. We use subscript i for i-th element. Superscript represents iteration steps (k for outer iteration and j for inner loop). For a vector v, ∥v∥ l0 , ∥v∥ l2 , and ∥v∥ l∞ denote l 0 -, l 2 -, and l ∞ -norms, respectively. supp(v) represents the nonzero elements of v. For a vector v ∈ R n , u = max{v, 0} denotesFor a matrix Φ ∈ R m×n and an index set A ⊆ {1, 2, • • • , n}, Φ A stands for the submatrix of Φ obtained by keeping only the columns indexed by A. Also, v A denotes the vector obtained by keeping only the components of a vector v ∈ R n indexed by A.

show abstract

“…σ > 1 increases the weights of the penalty parameters β 1,k , β 2,k in each iteration k, thus accelerating the numerical convergence speed of the proposed ADMM algorithm. A similar technique has been used in [14,29,57,58,69].…”

Section: Numerical Algorithmmentioning

confidence: 99%

Efficient Image Segmentation Framework with Difference of Anisotropic and Isotropic Total Variation for Blur and Poisson Noise Removal

Bui¹,

Lou²,

Park³

et al. 2023

Preprint

View full text Add to dashboard Cite

In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothingand-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.

show abstract

A Nonconvex Model with Minimax Concave Penalty for Image Restoration

Cited by 43 publications

References 40 publications

Forecasting the number of dengue fever based on weather conditions using ensemble forecasting method

Forecasting the number of dengue fever based on weather conditions using ensemble forecasting method

The first direct method of spot sparsity optimization for proton arc therapy

Efficient Image Segmentation Framework with Difference of Anisotropic and Isotropic Total Variation for Blur and Poisson Noise Removal

Contact Info

Product

Resources

About