799 research outputs found
Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
In this paper, we propose accurate and efficient finite difference methods to
discretize the two- and three-dimensional fractional Laplacian
() in hypersingular integral
form. The proposed finite difference methods provide a fractional analogue of
the central difference schemes to the fractional Laplacian, and as , they collapse to the central difference schemes of the classical Laplace
operator . We prove that our methods are consistent if ,
and the local truncation error is , with a small constant and denoting the floor function. If
, they can achieve the
second order of accuracy for any . These results hold for
any dimension and thus improve the existing error estimates for the
finite difference method of the one-dimensional fractional Laplacian. Extensive
numerical experiments are provided and confirm our analytical results. We then
apply our method to solve the fractional Poisson problems and the fractional
Allen-Cahn equations. Numerical simulations suggest that to achieve the second
order of accuracy, the solution of the fractional Poisson problem should {\it
at most} satisfy . One merit of our methods is
that they yield a multilevel Toeplitz stiffness matrix, an appealing property
for the development of fast algorithms via the fast Fourier transform (FFT).
Our studies of the two- and three-dimensional fractional Allen-Cahn equations
demonstrate the efficiency of our methods in solving the high-dimensional
fractional problems.Comment: 24 pages, 6 figures, and 6 table
Autonomous Swarm Navigation
Robotic swarm systems attract increasing attention in a wide variety of applications, where a multitude of self-organized robotic entities collectively accomplish sensing or exploration tasks. Compared to a single robot, a swarm system offers advantages in terms of exploration speed, robustness against single point of failures, and collective observations of spatio-temporal processes.
Autonomous swarm navigation, including swarm self-localization, the localization of external sources, and swarm control, is essential for the success of an autonomous swarm application. However, as a newly emerging technology, a thorough study of autonomous swarm navigation is still missing.
In this thesis, we systematically study swarm navigation systems, particularly emphasizing on their collective performance. The general theory of swarm navigation as well as an in-depth study on a specific swarm navigation system proposed for future Mars exploration missions are covered.
Concerning swarm localization, a decentralized algorithm is proposed, which achieves a near-optimal performance with low complexity for a dense swarm network.
Regarding swarm control, a position-aware swarm control concept is proposed. The swarm is aware of not only the position estimates and the estimation uncertainties of itself and the sources, but also the potential motions to enrich position information. As a result, the swarm actively adapts its formation to improve localization performance, without losing track of other objectives, such as goal approaching and collision avoidance.
The autonomous swarm navigation concept described in this thesis is verified for a specific Mars swarm exploration system. More importantly, this concept is generally adaptable to an extensive range of swarm applications
Power-Based Direction-of-Arrival Estimation Using a Single Multi-Mode Antenna
Phased antenna arrays are widely used for direction-of-arrival (DoA)
estimation. For low-cost applications, signal power or received signal strength
indicator (RSSI) based approaches can be an alternative. However, they usually
require multiple antennas, a single antenna that can be rotated, or switchable
antenna beams. In this paper we show how a multi-mode antenna (MMA) can be used
for power-based DoA estimation. Only a single MMA is needed and neither
rotation nor switching of antenna beams is required. We derive an estimation
scheme as well as theoretical bounds and validate them through simulations. It
is found that power-based DoA estimation with an MMA is feasible and accurate
Exploiting Image Local And Nonlocal Consistency For Mixed Gaussian-Impulse Noise Removal
Most existing image denoising algorithms can only deal with a single type of
noise, which violates the fact that the noisy observed images in practice are
often suffered from more than one type of noise during the process of
acquisition and transmission. In this paper, we propose a new variational
algorithm for mixed Gaussian-impulse noise removal by exploiting image local
consistency and nonlocal consistency simultaneously. Specifically, the local
consistency is measured by a hyper-Laplace prior, enforcing the local
smoothness of images, while the nonlocal consistency is measured by
three-dimensional sparsity of similar blocks, enforcing the nonlocal
self-similarity of natural images. Moreover, a Split-Bregman based technique is
developed to solve the above optimization problem efficiently. Extensive
experiments for mixed Gaussian plus impulse noise show that significant
performance improvements over the current state-of-the-art schemes have been
achieved, which substantiates the effectiveness of the proposed algorithm.Comment: 6 pages, 4 figures, 3 tables, to be published at IEEE Int. Conf. on
Multimedia & Expo (ICME) 201
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization
Recently, total variation (TV) based minimization algorithms have achieved
great success in compressive sensing (CS) recovery for natural images due to
its virtue of preserving edges. However, the use of TV is not able to recover
the fine details and textures, and often suffers from undesirable staircase
artifact. To reduce these effects, this letter presents an improved TV based
image CS recovery algorithm by introducing a new nonlocal regularization
constraint into CS optimization problem. The nonlocal regularization is built
on the well known nonlocal means (NLM) filtering and takes advantage of
self-similarity in images, which helps to suppress the staircase effect and
restore the fine details. Furthermore, an efficient augmented Lagrangian based
algorithm is developed to solve the above combined TV and nonlocal
regularization constrained problem. Experimental results demonstrate that the
proposed algorithm achieves significant performance improvements over the
state-of-the-art TV based algorithm in both PSNR and visual perception.Comment: 4 Pages, 1 figures, 3 tables, to be published at IEEE Int. Symposium
of Circuits and Systems (ISCAS) 201
Image Super-Resolution via Dual-Dictionary Learning And Sparse Representation
Learning-based image super-resolution aims to reconstruct high-frequency (HF)
details from the prior model trained by a set of high- and low-resolution image
patches. In this paper, HF to be estimated is considered as a combination of
two components: main high-frequency (MHF) and residual high-frequency (RHF),
and we propose a novel image super-resolution method via dual-dictionary
learning and sparse representation, which consists of the main dictionary
learning and the residual dictionary learning, to recover MHF and RHF
respectively. Extensive experimental results on test images validate that by
employing the proposed two-layer progressive scheme, more image details can be
recovered and much better results can be achieved than the state-of-the-art
algorithms in terms of both PSNR and visual perception.Comment: 4 pages, 4 figures, 1 table, to be published at IEEE Int. Symposium
of Circuits and Systems (ISCAS) 201
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