scholarly journals A General Proximal Alternating Minimization Method with Application to Nonconvex Nonsmooth 1D Total Variation Denoising

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Xiaoya Zhang ◽  
Tao Sun ◽  
Lizhi Cheng
Keyword(s):  
Total Variation ◽  
Auxiliary Variable ◽  
Alternating Minimization ◽  
Minimization Method ◽  
Systematic Analysis ◽  
Nonsmooth Problems ◽  
Alternating Minimization Algorithm ◽  
Wide Range ◽  
Total Variation Denoising ◽  
Signal Image

We deal with a class of problems whose objective functions are compositions of nonconvex nonsmooth functions, which has a wide range of applications in signal/image processing. We introduce a new auxiliary variable, and an efficient general proximal alternating minimization algorithm is proposed. This method solves a class of nonconvex nonsmooth problems through alternating minimization. We give a brilliant systematic analysis to guarantee the convergence of the algorithm. Simulation results and the comparison with two other existing algorithms for 1D total variation denoising validate the efficiency of the proposed approach. The algorithm does contribute to the analysis and applications of a wide class of nonconvex nonsmooth problems.

scholarly journals A Fast High-Order Total Variation Minimization Method for Multiplicative Noise Removal

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiao-Guang Lv ◽  
Jiang Le ◽  
Jin Huang ◽  
Liu Jun
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
Noise Removal ◽  
High Order ◽  
Alternating Minimization ◽  
Minimization Method ◽  
Total Variation Minimization ◽  
Alternating Minimization Algorithm ◽  
Staircase Effect ◽  
Multiplicative Noise Removal

Multiplicative noise removal problem has received considerable attention in recent years. The total variation regularization method for the solution of the noise removal problem can preserve edges well but has the sometimes undesirable staircase effect. In this paper, we propose a fast high-order total variation minimization method to restore multiplicative noisy images. The proposed method is able to preserve edges and at the same time avoid the staircase effect in the smooth regions. An alternating minimization algorithm is employed to solve the proposed high-order total variation minimization problem. We discuss the convergence of the alternating minimization algorithm. Some numerical results show that the proposed method gives restored images of higher quality than some existing multiplicative noise removal methods.

scholarly journals Relative Total Variation Structure Analysis-Based Fusion Method for Hyperspectral and LiDAR Data Classification

2021 ◽  
Vol 13 (6) ◽  
pp. 1143
Author(s):  
Yinghui Quan ◽  
Yingping Tong ◽  
Wei Feng ◽  
Gabriel Dauphin ◽  
Wenjiang Huang ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Total Variation ◽  
Structure Analysis ◽  
Hyperspectral Image ◽  
Gabor Filter ◽  
Heterogeneous Data ◽  
Lidar Data ◽  
Fusion Method ◽  
Wide Range ◽  
Relative Total Variation

The fusion of the hyperspectral image (HSI) and the light detecting and ranging (LiDAR) data has a wide range of applications. This paper proposes a novel feature fusion method for urban area classification, namely the relative total variation structure analysis (RTVSA), to combine various features derived from HSI and LiDAR data. In the feature extraction stage, a variety of high-performance methods including the extended multi-attribute profile, Gabor filter, and local binary pattern are used to extract the features of the input data. The relative total variation is then applied to remove useless texture information of the processed data. Finally, nonparametric weighted feature extraction is adopted to reduce the dimensions. Random forest and convolutional neural networks are utilized to evaluate the fusion images. Experiments conducted on two urban Houston University datasets (including Houston 2012 and the training portion of Houston 2017) demonstrate that the proposed method can extract the structural correlation from heterogeneous data, withstand a noise well, and improve the land cover classification accuracy.

scholarly journals Recent Advances in Unmanned Aerial Vehicle Forest Remote Sensing—A Systematic Review. Part I: A General Framework

Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 327 ◽  
Author(s):  
Riccardo Dainelli ◽  
Piero Toscano ◽  
Salvatore Filippo Di Gennaro ◽  
Alessandro Matese
Keyword(s):  
Remote Sensing ◽  
Unmanned Aerial Vehicle ◽  
Relevant Information ◽  
Forest Monitoring ◽  
Machine Learning Techniques ◽  
Planted Forests ◽  
Systematic Analysis ◽  
Aerial Photogrammetry ◽  
Wide Range ◽  
Aerial Vehicle

Natural, semi-natural, and planted forests are a key asset worldwide, providing a broad range of positive externalities. For sustainable forest planning and management, remote sensing (RS) platforms are rapidly going mainstream. In a framework where scientific production is growing exponentially, a systematic analysis of unmanned aerial vehicle (UAV)-based forestry research papers is of paramount importance to understand trends, overlaps and gaps. The present review is organized into two parts (Part I and Part II). Part II inspects specific technical issues regarding the application of UAV-RS in forestry, together with the pros and cons of different UAV solutions and activities where additional effort is needed, such as the technology transfer. Part I systematically analyzes and discusses general aspects of applying UAV in natural, semi-natural and artificial forestry ecosystems in the recent peer-reviewed literature (2018–mid-2020). The specific goals are threefold: (i) create a carefully selected bibliographic dataset that other researchers can draw on for their scientific works; (ii) analyze general and recent trends in RS forest monitoring (iii) reveal gaps in the general research framework where an additional activity is needed. Through double-step filtering of research items found in the Web of Science search engine, the study gathers and analyzes a comprehensive dataset (226 articles). Papers have been categorized into six main topics, and the relevant information has been subsequently extracted. The strong points emerging from this study concern the wide range of topics in the forestry sector and in particular the retrieval of tree inventory parameters often through Digital Aerial Photogrammetry (DAP), RGB sensors, and machine learning techniques. Nevertheless, challenges still exist regarding the promotion of UAV-RS in specific parts of the world, mostly in the tropical and equatorial forests. Much additional research is required for the full exploitation of hyperspectral sensors and for planning long-term monitoring.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

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