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adaptive complexity for Pixel-Value-Ordering Based Reversible Data Hiding

IEEE SIGNAL PROCESSING LETTERS 2020年 27卷 915-919页

作者： Pan, Zhibin Gao, Xinyi Gao, Erdun Fan, Guojun Xi An Jiao Tong Univ Fac Elect & Informat Engn Sch Elect & Informat Engn Xian 710049 Peoples R China CAST Natl Key Lab Sci & Technol Space Microwave Xian 710100 Peoples R China

Pixel-value-ordering (PVO) is a widely used reversible data hiding (RDH) framework which aims to achieve the high quality of stego-image under low capacity. In this letter, we propose a general location-based adaptive complexity for PVO. Different from the block-based complexity in the previous PVO-based methods, our proposed method adaptively selects context pixels from the perspective of the relative locations of predicted pixel and prediction pixel. Consequently, different number of high correlation context pixels can be adaptively selected and the context pixels can break the limitation of the current block. Moreover, instead of sharing the same block complexity by two predicted pixels in the current block, each predicted pixel can be utilized independently according to its own corresponding complexity. Our proposed adaptive complexity can combine with any PVO-based methods and the experimental results show that our proposed method achieves a significant improvement in prediction accuracy and embedding performance.

关键词： complexity theory Correlation Distortion Interference Media Sorting Fans Reversible data hiding pixel-value-ordering predicted pixels prediction pixels context pixels adaptive complexity

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Deterministic approximation algorithm for submodular maximization subject to a matroid constraint

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INTERNATIONAL JOURNAL OF CARDIOLOGY 2021年 343卷 1-15页

作者： Sun, Xin Xu, Dachuan Guo, Longkun Li, Min Beijing Univ Technol Dept Operat Res & Informat Engn Beijing 100124 Peoples R China Qilu Univ Technol Shandong Comp Sci Ctr Sch Comp Sci & Technol Shandong Key Lab Comp NetworksShandong Acad Sci Jinan 250353 Peoples R China Fuzhou Univ Sch Comp & Data Sci Fuzhou 350116 Peoples R China Shandong Normal Univ Sch Math & Stat Jinan 250014 Peoples R China

In this paper, we study the generalized submodular maximization problem with a nonnegative monotone submodular set function as the objective function and subject to a matroid constraint. The problem is generalized through the curvature parameter alpha is an element of [0, 1] which measures how far a set function deviates from linearity to submodularity. We propose a deterministic approximation algorithm which uses the approximation algorithm proposed by Buchbinder et al. [2] as a building block and inherits the approximation guarantee for alpha = 1. For general value of the curvature parameter alpha is an element of [0, 1], we present an approximation algorithm with a factor of 1+h(alpha)(y)+Delta.[3+alpha-(2+alpha)y-(1+alpha)h(alpha)(y)]/2+alpha+(1+alpha)(1-y), where y is an element of [0, 1] is a predefined parameter for tuning the ratio. In particular, when alpha = 1 we obtain a ratio 0.5008 when setting y = 0.9, coinciding with the renowned state-of-art approximate ratio; when alpha = 0 that the object is a linear function, the approximation factor equals one and our algorithm is indeed an exact algorithm that always produces optimum solutions. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Approximation algorithm Submodular maximization Total curvature Matroid constraint Deterministic algorithm adaptive complexity SET OPTIMIZATION

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On the performance of particle filters with adaptive number of particles

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STATISTICS AND COMPUTING 2021年第6期31卷 1-18页

作者： Elvira, Victor Miguez, Joaquin Djuric, Petar M. Univ Edinburgh Sch Math Edinburgh Midlothian Scotland Univ Carlos III Madrid Dept Signal Theory & Commun Madrid Spain IIS Gregorio Maranon Madrid Spain SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA Alan Turing Inst London England

We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models. To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al. (IEEE Trans Signal Process 65(7):1781-1794, 2017). In this class of algorithms, the number of Monte Carlo samples (known as particles) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles. The evaluation of the predictive statistics that lies at the core of the methodology is done by generating fictitious observations, i.e., particles in the observation space. We study, both analytically and numerically, the impact of the number K of these particles on the performance of the algorithm. In particular, we prove that if the predictive statistics with K fictitious observations converged exactly, then the particle approximation of the filtering distribution would match the first K elements in a series of moments of the true filter. This result can be understood as a converse to some convergence theorems for PFs. From this analysis, we deduce an alternative predictive statistic that can be computed (for some models) without sampling any fictitious observations at all. Finally, we conduct an extensive simulation study that illustrates the theoretical results and provides further insights into the complexity, performance and behavior of the new class of algorithms.

关键词： Particle filtering Sequential Monte Carlo Predictive distributions Convergence analysis adaptive complexity

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Flexible patch moving modes for pixel-value-ordering based reversible data hiding methods

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EXPERT SYSTEMS WITH APPLICATIONS 2023年 214卷

作者： Fan, Guojun Pan, Zhibin Zhou, Quan Zhang, Xiaoran Xi An Jiao Tong Univ Fac Elect & Informat Engn Xian 710049 Peoples R China China Acad Space Technol Natl Key Lab Sci & Technol Space Microwave Xian 710100 Peoples R China Xi An Jiao Tong Univ Res Inst Xian 311215 Zhejiang Peoples R China

Pixel-value-ordering (PVO) is one of the most popular frameworks in the research of reversible data hiding (RDH) in recent years. In most PVO-based methods, the cover image is divided into non-overlapped blocks to embed secret data into the maximum and minimum pixels of each block. In these methods, the image division processing is just like moving a patch with constant step lengths in both horizontal and vertical directions. As a result, the block amount, as well as the embedding capacity (EC), is limited by the image size and the patch size. In this paper, we propose one-dimensional and two-dimensional flexible patch moving (FPM) modes to move the patch with adaptive step lengths. After enlarging the EC by employing FPM, an average-difference-based complexity computation is also proposed to cooperate with FPM to further improve the embedding performance. Finally, multiple pairwise embedding schemes are adaptively applied on blocks with different complexities to enhance the embedding performance once again. Experimental results illustrate that the proposed FPM modes work well on many PVO-based methods. Moreover, the proposed method achieves an obvious improvement in fidelity when compared with some state-of-the-art RDH schemes.

关键词： Reversible data hiding Pixel -value -ordering Flexible patch moving adaptive complexity Pairwise modification

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A note for approximating the submodular cover problem over integer lattice with low adaptive and query complexities

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INFORMATION PROCESSING LETTERS 2023年 182卷

作者： Pham, Canh, V Ha, Dung T. K. Phenikaa Univ ORLab Hanoi 12116 Vietnam Vietnam Natl Univ Univ Engn & Technol Fac Informat Technol Hanoi 10000 Vietnam

This paper studies the Diminishing Return Submodular Cover (DRSC) problem as follows: given a diminishing return submodular function f :Z(+)(E)-> R+ over the ground set E of size n, a positive integer B as the maximum value of a coordinate of a vector in Z(+)(E) and a threshold alpha > 0, the problem asks to find the vector with the smallest size x so that f(x) >= alpha. This problem has been attracted by much research recently due to its importance in machine learning and combinatorial optimization. However, because of high query and adaptive complexities, the existing algorithms might still not be efficient enough when working with large input data. This paper proposes a randomized and bicriteria approximation algorithm that has O (log n) adaptive complexity and O ((n + log n log B) log(nB)) query complexity. Our algorithm significantly reduces both adaptive and query complexities compared to some state-of-the-art algorithms by factors of Omega(log(m) log(2)(mn log B)(1 + log(log B)/ log(n))), Omega(min{n/ log(n),log(B)}) respectively, where m = f (B center dot 1). (c) 2023 Elsevier B.V. All rights reserved.

关键词： submodular Cover integer lattice adaptive complexity approximation algorithms

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The complexity of subdivision for diameter-distance tests

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JOURNAL OF SYMBOLIC COMPUTATION 2020年 101卷 1-27页

作者： Burr, Michael Gao, Shuhong Tsigaridas, Elias Clemson Univ Sch Math & Stat Sci Clemson SC 29634 USA UPMC Univ Paris 06 Sorbonne Univ CNRS INRIALab Informat Paris 6 LIP6Equipe PolSys 4 Pl Jussieu F-75252 Paris 05 France

We present a general framework for analyzing the complexity of subdivision-based algorithms whose tests are based on the sizes of regions and their distance to certain sets (often varieties) intrinsic to the problem under study. We call such tests diameter-distance tests. We illustrate that diameter-distance tests are common in the literature by proving that many interval arithmetic-based tests are, in fact, diameter-distance tests. For this class of algorithms, we provide both non-adaptive bounds for the complexity, based on separation bounds, as well as adaptive bounds, by applying the framework of continuous amortization. Using this structure, we provide the first complexity analysis for the algorithm by Plantinga and Vegeter for approximating real implicit curves and surfaces. We present both adaptive and nonadaptive a prioriworst-case bounds on the complexity of this algorithm both in terms of the number of subregions constructed and in terms of the bit complexity for the construction. Finally, we construct families of hypersurfaces to prove that our bounds are tight. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Algorithmic complexity Worst case bit-complexity Subdivision algorithms Continuous amortization adaptive complexity Separation bounds

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A comparative study between PVO-based framework and multi-predictor mechanism in reversible data hiding*

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JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION 2021年 81卷

作者： Fan, Guojun Pan, Zhibin Zhou, Quan Gao, Xinyi Zhang, Xiaoran Xi An Jiao Tong Univ Fac Elect & Informat Engn Xian 710049 Peoples R China China Acad Space Technol Natl Key Lab Sci & Technol Space Microwave Xian 710100 Peoples R China

Sorting-based reversible data hiding (RDH) methods like pixel-value-ordering (PVO) can predict pixel values accurately and achieve an extremely low distortion on the embedded image. However, the excellent performance of these methods was not well explained in previous works, and there are unexploited common points among them. In this paper, we propose a general multi-predictor (GMP) framework to summarize PVO-based RDH methods and explain their high prediction accuracy. Moreover, by utilizing the proposed GMP framework, a more efficient sorting-based RDH method is given as an example to show the generality and applicability of our framework. Comparing with other PVO-based methods, the proposed example method can achieve significant improvement in embedding performance. It is hopeful that more efficient sorting-based RDH algorithms can be designed according to our proposed framework by designing better predictors and their combination methods.

关键词： Reversible data hiding General multi-predictor framework Pixel-value-ordering (PVO) Additional predictors adaptive complexity

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complexity, adaptive complexity and the Creative View of natural selection

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STUDIES IN HISTORY AND PHILOSOPHY OF SCIENCE PART C-STUDIES IN HISTORY AND PHILOSOPHY OF BIOLOGICAL AND BIOMEDICAL SCIENCES 2013年第3期44卷 312-315页

作者： Razeto-Barry, Pablo IFICC Inst Filosofia & Ciencias Complejidad Santiago 3024 Chile Univ Diego Portales Vicerrectoria Acad Santiago Chile

In this paper, I respond to arguments proposed by Brunnander in this journal issue concerning my position regarding the Creative View of natural selection (Razeto-Barry & Frick, 2011). Brunnander argues that (i) the Creative View we defend does not serve to answer William Paley's question because (ii) Paley's question is "why there are complex things rather than simple ones'' and (iii) natural selection cannot answer this question. Brunnander's arguments for (iii) defend a Non-creative View of natural selection (sensu Razeto-Barry & Frick, 2011). Here I claim that Brunnander's arguments for (iii) are mistaken and I also argue that even accepting (iii) we do not have to accept (i), given that statement (ii) is historically and conceptually flawed. Thus here I analyze Paley's question from a historical point of view and from a contemporary perspective in a quest for the potential conceptual relevance of Paley's question today. In this vein I argue that from a contemporary point of view statement (iii) may be correct but for different reasons than those adduced by Brunnander. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Contrastive explanation Creative View Paley's question complexity adaptive complexity

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Adapting the Number of Particles in Sequential Monte Carlo Methods Through an Online Scheme for Convergence Assessment

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第7期65卷 1781-1794页

作者： Elvira, Victor Miguez, Joaquin Djuric, Petar M. IMT Lille Douai CRIStAL UMR CNRS 9189 F-59655 Villeneuve Dascq France Univ Carlos III Madrid Dept Signal Theory & Commun Madrid 28911 Spain SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters in an onlinemanner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz 63 system.

关键词： Particle filtering sequential Monte Carlo convergence assessment predictive distribution convergence analysis computational complexity adaptive complexity

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ONLINE ADAPTATION OF THE NUMBER OF PARTICLES OF SMC METHODS 41

ONLINE ADAPTATION OF THE NUMBER OF PARTICLES OF SMC METHODS

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Elvira, Victor Miguez, Joaquin Djuric, Petar M. Univ Carlos III Madrid Dept Signal Theory & Commun Leganes 28911 Spain Queen Mary Univ Sch Math Sci London E1 4NS England SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA

ISBN: (纸本)9781479999880

Particle filtering is a widely used sequential methodology that approximates probability distributions by using discrete random measures composed of weighted particles. A large number of particles improves the quality of the approximation but increases the computational requirements. Although there exists an abundant variety of particle filtering algorithms in the literature, there is lack of work devoted to selecting or adapting the number of particles systematically. In this paper we propose a novel methodology for online assessment of convergence of particle filtering. Based on theoretical analysis of the assessment, we propose an algorithm for the adaptation of the number of particles in online manner. The performance of the proposed algorithm is demonstrated for two state- space models.

关键词： Particle filtering sequential Monte Carlo convergence assessment predictive distribution convergence analysis computational complexity adaptive complexity

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