scholarly journals A LogTVSCAD Nonconvex Regularization Model for Image Deblurring in the Presence of Impulse Noise

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Zhijun Luo ◽  
Zhibin Zhu ◽  
Benxin Zhang
Keyword(s):  
Impulsive Noise ◽  
Poor Performance ◽  
Absolute Deviation ◽  
Difference Of Convex Functions ◽  
Alternating Direction ◽  
Impulsive Noises ◽  
Nonconvex Regularization ◽  
Difference Of Convex ◽  
High Level ◽  
Nonconvex Model

This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log-function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data-fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for high-level impulsive noise. A difference of convex functions algorithm (DCA) is proposed to solve the nonconvex model. For the model subproblem, we consider the alternating direction method of multipliers (ADMM) algorithm to solve it. The global convergence is discussed based on Kurdyka–Lojasiewicz. Experimental results show the advantages of the proposed nonconvex model over existing models.

Alternating direction method of multipliers with difference of convex functions

2017 ◽  
Vol 44 (3) ◽  
pp. 723-744 ◽  
Author(s):  
Tao Sun ◽  
Penghang Yin ◽  
Lizhi Cheng ◽  
Hao Jiang
Keyword(s):  
Convex Functions ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Difference Of Convex Functions ◽  
Alternating Direction ◽  
Difference Of Convex

scholarly journals An Efficient Method for Convex Constrained Rank Minimization Problems Based on DC Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wanping Yang ◽  
Jinkai Zhao ◽  
Fengmin Xu
Keyword(s):  
Objective Function ◽  
Minimization Problem ◽  
Dc Programming ◽  
Rank Minimization ◽  
Closed Form Solutions ◽  
Minimization Problems ◽  
Difference Of Convex Functions ◽  
Convex Objective Function ◽  
Difference Of Convex ◽  
Cut Problems

The constrained rank minimization problem has various applications in many fields including machine learning, control, and signal processing. In this paper, we consider the convex constrained rank minimization problem. By introducing a new variable and penalizing an equality constraint to objective function, we reformulate the convex objective function with a rank constraint as a difference of convex functions based on the closed-form solutions, which can be reformulated as DC programming. A stepwise linear approximative algorithm is provided for solving the reformulated model. The performance of our method is tested by applying it to affine rank minimization problems and max-cut problems. Numerical results demonstrate that the method is effective and of high recoverability and results on max-cut show that the method is feasible, which provides better lower bounds and lower rank solutions compared with improved approximation algorithm using semidefinite programming, and they are close to the results of the latest researches.

Fast Algorithms for LS and LAD-Collaborative Regression

2021 ◽  
Author(s):  
Jun Sun ◽  
Lingchen Kong ◽  
Mei Li
Keyword(s):  
Numerical Experiments ◽  
Modern Science ◽  
Alternating Direction Method ◽  
Least Square ◽  
High Dimensional ◽  
Statistical Interpretation ◽  
Absolute Deviation ◽  
Linear Rate ◽  
Alternating Direction ◽  
High Dimensional Datasets

With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.

Control Integration Mechanisms

1994 ◽  
Author(s):  
Alan W. Brown ◽  
David J. Carney ◽  
Edwin J. Morris ◽  
Dennis B. Smith ◽  
Paul F. Zarrella
Keyword(s):  
Traditional Approach ◽  
Poor Performance ◽  
Tool Integration ◽  
Source File ◽  
Data Schema ◽  
Integration Approach ◽  
Control Signals ◽  
Primary Means ◽  
High Level ◽  
Control Integration

Controlling and coordinating tool interactions in a CASE environment require an approach to tool integration that is sufficiently flexible and adaptable to suit different user needs, as well as simple and efficient. These conditions will ensure that new tools can easily be integrated and that their productivity is not significantly impaired. As discussed in the previous chapter, one traditional approach toward tool integration has been based on data sharing, often through a common database in which all tools deposit their data. While this approach can provide a high level of control and coordination between tools, it also imposes a significant overhead on the tools, both because of poor performance of existing database mechanisms when used in this way, and because of the necessary agreement required between the tools to define a common syntax and semantics for their data (e.g., a common data schema). Another approach to integration has been called the control integration approach. This approach is based on viewing a CASE environment as a collection of services provided by different tools. Actions carried out by a tool are announced to other tools via control signals. The tools receiving such signals can decide if the other tool’s actions require that they take any actions themselves. For example, when an editing tool announces that changes have been made to a source file, a build tool may receive this information and initiate a new system build. In addition, one tool may directly request that another tool perform an action by sending it a control signal. For example, the build tool may request that the source file be compiled by a particular compiler. Hence, the primary means of coordination between tools is through the sending and receiving of control signals. In the rest of this chapter, we examine the notion of control integration in a CASE environment, review a number of existing systems, and analyze those systems to identify their differences and to reveal interesting future directions for this work. The reviewed systems do not represent an exhaustive examination of systems implementing a control integration approach.

scholarly journals The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functions

2020 ◽  
Vol 30 (1) ◽  
pp. 980-1006 ◽  
Author(s):  
Francisco J. Aragón Artacho ◽  
Phan T. Vuong
Keyword(s):  
Convex Functions ◽  
Nonsmooth Functions ◽  
Difference Of Convex Functions ◽  
Difference Of Convex

Diagnoses

1988 ◽  
Vol 13 (3) ◽  
pp. 64-72
Keyword(s):  
Resource Allocation ◽  
Poor Performance ◽  
State Intervention ◽  
Import Duty ◽  
Pricing Policies ◽  
Performance Pricing ◽  
Main Input ◽  
High Level ◽  
The Cost ◽  
Case Data

The diagnostic case, BTR Ltd., Rampur, UP, raised many questions such as reasons for BTR's poor performance, pricing policies of the Consortium of producers of which BTR was a member, and the implications of state intervention in pricing and allocation of resin, the main input. In this Diagnoses feature, experts from both practising and academic worlds examine these and other questions. Vederah, Dholakia, and Sandesara argue, based on the analysis of case data, that the relatively poor performance of BTR has more to do with its own inefficiency than with the rosin prices fixed by the Consortium. They suggest the areas where BTR should improve its performance and comment on how the Consortium could strengthen and redefine its role. Gurdev Singh develops a framework for evaluating state intervention and applies it to the various stages of resin processing. Vederah's comparison of the cost of imported and indigenous rosin shows how neglected the interests of the users are. The high level of protective import duty and the inadequacy of resource allocation for improvement of production and productivity point to the need for coordinated strategies that take account of both producers and users.

The profitability of herding: evidence from Taiwan

2018 ◽  
Vol 44 (7) ◽  
pp. 919-934 ◽  
Author(s):  
Chun-Da Chen ◽  
Riza Demirer
Keyword(s):  
Design Methodology ◽  
State Space Model ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Past Performance ◽  
Absolute Deviation ◽  
Cross Sectional ◽  
Content Type ◽  
Space Model ◽  
High Level

Purpose The purpose of this paper is to show that the level of herding in an industry can be the basis for a profitable investment strategy. Design/methodology/approach The authors apply three different herding measures in the paper, including cross-sectional standard deviation, cross-sectional absolute deviation and non-linear model – state–space model. Findings The authors find that industries that experience a high level of herding yield higher subsequent returns regardless of their past performance. Consequently, the authors show that a herding-based investment strategy generates significant profits, even after adjusting for risk. The findings also show that the herding effect when combined with past performance as part of a conditional investment strategy yields significant profits regardless of the formation and holding periods. The findings suggest that the level of herding could serve as a systematic driver of returns and could be exploited for profitable investment strategies. Originality/value To the best of authors’ knowledge, this is the first study in the literature to show that herding by itself can serve as a determinant of returns regardless of past performance.

Online Learning Based on Online DCA and Application to Online Classification

2020 ◽  
Vol 32 (4) ◽  
pp. 759-793 ◽  
Author(s):  
Hoai An Le Thi ◽  
Vinh Thanh Ho
Keyword(s):  
Online Learning ◽  
State Of The Art ◽  
Classification Algorithms ◽  
Data Sets ◽  
Prediction Problem ◽  
Dc Algorithm ◽  
Difference Of Convex Functions ◽  
Online Classification ◽  
Learning Techniques ◽  
Difference Of Convex

We investigate an approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for online learning techniques. The prediction problem of an online learner can be formulated as a DC program for which online DCA is applied. We propose the two so-called complete/approximate versions of online DCA scheme and prove their logarithmic/sublinear regrets. Six online DCA-based algorithms are developed for online binary linear classification. Numerical experiments on a variety of benchmark classification data sets show the efficiency of our proposed algorithms in comparison with the state-of-the-art online classification algorithms.

scholarly journals Efficient Impulsive Noise Mitigation for OFDM Systems Using the Alternating Direction Method of Multipliers

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xin-Rong Lv ◽  
Youming Li ◽  
Yu-Cheng He
Keyword(s):  
Optimization Problem ◽  
Impulsive Noise ◽  
Estimation Algorithm ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Ofdm Systems ◽  
Box Constraints ◽  
Noise Mitigation ◽  
Alternating Direction ◽  
Performance Gains

An efficient impulsive noise estimation algorithm based on alternating direction method of multipliers (ADMM) is proposed for OFDM systems using quadrature amplitude modulation (QAM). Firstly, we adopt the compressed sensing (CS) method based on the l1-norm optimization to estimate impulsive noise. Instead of the conventional methods that exploit only the received signal in null tones as constraint, we add the received signal of data tones and QAM constellations as constraints. Then a relaxation approach is introduced to convert the discrete constellations to the convex box constraints. After that a linear programming is used to solve the optimization problem. Finally, a framework of ADMM is developed to solve the problem in order to reduce the computation complexity. Simulation results for 4-QAM and 16-QAM demonstrate the practical advantages of the proposed algorithm over the other algorithms in bit error rate performance gains.

A Difference of Convex Functions Approach to Large-Scale Log-Linear Model Estimation

2013 ◽  
Vol 21 (11) ◽  
pp. 2255-2266 ◽  
Author(s):  
Theodoros Tsiligkaridis ◽  
Etienne Marcheret ◽  
Vaibhava Goel
Keyword(s):  
Linear Model ◽  
Convex Functions ◽  
Large Scale ◽  
Model Estimation ◽  
Difference Of Convex Functions ◽  
Difference Of Convex ◽  
Log Linear
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