Ray Tracing Acceleration using Total Variation Norm Minimization for Radio Map Simulation

2020 ◽  
pp. 1-1
Author(s):  
Norisato Suga ◽  
Ryohei Sasaki ◽  
Makoto Osawa ◽  
Toshihiro Furukawa
Keyword(s):  
Ray Tracing ◽  
Total Variation ◽  
Total Variation Norm ◽  
Norm Minimization ◽  
Variation Norm ◽  
Radio Map

scholarly journals Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity

2014 ◽  
Vol 51 (3) ◽  
pp. 756-768 ◽  
Author(s):  
Servet Martínez ◽  
Jaime San Martín ◽  
Denis Villemonais
Keyword(s):  
Total Variation ◽  
Existence And Uniqueness ◽  
Initial Distribution ◽  
Total Variation Norm ◽  
Birth And Death Processes ◽  
Long Time Behaviour ◽  
Long Time ◽  
Unique Distribution ◽  
Variation Norm ◽  
Quasistationary Distributions

We study the long-time behaviour of a Markov process evolving in N and conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a unique quasistationary distribution (in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in law to a unique distribution ρ supported in N* if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes.

scholarly journals Total Variation Applications in Computer Vision

2018 ◽  
pp. 543-570
Author(s):  
Vania Vieira Estrela ◽  
Hermes Aguiar Magalhães ◽  
Osamu Saotome
Keyword(s):  
Computer Vision ◽  
Total Variation ◽  
Total Variation Norm ◽  
Mathematical Background ◽  
Tv Regularization ◽  
Variation Norm ◽  
Image Processing Algorithms ◽  
Processing Algorithms ◽  
Set Up

The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii) to set up a brief discussion on the mathematical background of TV methods; and (iv) to establish a relationship between models and a few existing methods to solve problems cast as TV-norm. For the most part, image-processing algorithms blur the edges of the estimated images, however TV regularization preserves the edges with no prior information on the observed and the original images. The regularization scalar parameter λ controls the amount of regularization allowed and it is essential to obtain a high-quality regularized output. A wide-ranging review of several ways to put into practice TV regularization as well as its advantages and limitations are discussed.

scholarly journals Total Variation Applications in Computer Vision

2016 ◽  
pp. 41-64 ◽  
Author(s):  
Vania Vieira Estrela ◽  
Hermes Aguiar Magalhães ◽  
Osamu Saotome
Keyword(s):  
Computer Vision ◽  
Total Variation ◽  
Total Variation Norm ◽  
Mathematical Background ◽  
Tv Regularization ◽  
Variation Norm ◽  
Image Processing Algorithms ◽  
Processing Algorithms ◽  
Set Up

The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii) to set up a brief discussion on the mathematical background of TV methods; and (iv) to establish a relationship between models and a few existing methods to solve problems cast as TV-norm. For the most part, image-processing algorithms blur the edges of the estimated images, however TV regularization preserves the edges with no prior information on the observed and the original images. The regularization scalar parameter ? controls the amount of regularization allowed and it is essential to obtain a high-quality regularized output. A wide-ranging review of several ways to put into practice TV regularization as well as its advantages and limitations are discussed.

scholarly journals Weak Precompactness in the Space of Vector-Valued Measures of Bounded Variation

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ioana Ghenciu
Keyword(s):  
Banach Space ◽  
Total Variation ◽  
Bounded Variation ◽  
Measure Space ◽  
Total Variation Norm ◽  
Variation Norm ◽  
Additive Measures ◽  
Vector Valued

For a Banach spaceXand a measure space(Ω,Σ), letM(Ω,X)be the space of allX-valued countably additive measures on(Ω,Σ)of bounded variation, with the total variation norm. In this paper we give a characterization of weakly precompact subsets ofM(Ω,X).

scholarly journals Linear Total Variation Approximate Regularized Nuclear Norm Optimization for Matrix Completion

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xu Han ◽  
Jiasong Wu ◽  
Lu Wang ◽  
Yang Chen ◽  
Lotfi Senhadji ◽  
...  
Keyword(s):  
Total Variation ◽  
Missing Values ◽  
Matrix Completion ◽  
Nuclear Norm ◽  
Low Rank ◽  
Visual Data ◽  
Total Variation Norm ◽  
Rank Matrix ◽  
Variation Norm ◽  
Low Rank Matrix

Matrix completion that estimates missing values in visual data is an important topic in computer vision. Most of the recent studies focused on the low rank matrix approximation via the nuclear norm. However, the visual data, such as images, is rich in texture which may not be well approximated by low rank constraint. In this paper, we propose a novel matrix completion method, which combines the nuclear norm with the local geometric regularizer to solve the problem of matrix completion for redundant texture images. And in this paper we mainly consider one of the most commonly graph regularized parameters: the total variation norm which is a widely used measure for enforcing intensity continuity and recovering a piecewise smooth image. The experimental results show that the encouraging results can be obtained by the proposed method on real texture images compared to the state-of-the-art methods.

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