12 research outputs found
Periodic solutions for a porous medium equation
In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions
LP-BFGS attack: An adversarial attack based on the Hessian with limited pixels
Deep neural networks are vulnerable to adversarial attacks. Most white-box
attacks are based on the gradient of models to the input. Since the computation
and memory budget, adversarial attacks based on the Hessian information are not
paid enough attention. In this work, we study the attack performance and
computation cost of the attack method based on the Hessian with a limited
perturbation pixel number. Specifically, we propose the Limited Pixel BFGS
(LP-BFGS) attack method by incorporating the BFGS algorithm. Some pixels are
selected as perturbation pixels by the Integrated Gradient algorithm, which are
regarded as optimization variables of the LP-BFGS attack. Experimental results
across different networks and datasets with various perturbation pixel numbers
demonstrate our approach has a comparable attack with an acceptable computation
compared with existing solutions.Comment: 5 pages, 4 figure
Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation
Variational level set method has become a powerful tool in image segmentation
due to its ability to handle complex topological changes and maintain
continuity and smoothness in the process of evolution. However its evolution
process can be unstable, which results in over flatted or over sharpened
contours and segmentation failure. To improve the accuracy and stability of
evolution, we propose a high-order level set variational segmentation method
integrated with molecular beam epitaxy (MBE) equation regularization. This
method uses the crystal growth in the MBE process to limit the evolution of the
level set function, and thus can avoid the re-initialization in the evolution
process and regulate the smoothness of the segmented curve. It also works for
noisy images with intensity inhomogeneity, which is a challenge in image
segmentation. To solve the variational model, we derive the gradient flow and
design scalar auxiliary variable (SAV) scheme coupled with fast Fourier
transform (FFT), which can significantly improve the computational efficiency
compared with the traditional semi-implicit and semi-explicit scheme. Numerical
experiments show that the proposed method can generate smooth segmentation
curves, retain fine segmentation targets and obtain robust segmentation results
of small objects. Compared to existing level set methods, this model is
state-of-the-art in both accuracy and efficiency
Asymptotic Behavior of Solutions of a Periodic Diffusion Equation
<p/> <p>We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic solutions, that is, all non-trivial nonnegative solutions of the initial boundary value problem, will lie between a minimal and a maximal nonnegative nontrivial periodic solutions, as time tends to infinity.</p
A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations
We consider a cooperating two-species Lotka-Volterra model of degenerate
parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system
A New Variational Model for Segmenting Objects of Interest from Color Images
We propose a new variational model for segmenting objects of interest from color images. This model is inspired by the geodesic active contour model, the region-scalable fitting model, the weighted bounded variation model and the active contour models based on the Mumford-Shah model. In order to segment desired objects in color images, the energy functional in our model includes a discrimination function that determines whether an image pixel belongs to the desired objects or not. Compared with other active contour models, our new model cannot only avoid the usual drawback in the level set approach but also detect the objects of interest accurately. Moreover, we investigate the new model mathematically and establish the existence of the minimum to the new energy functional. Finally, numerical results show the effectiveness of our proposed model
A Fractional-Order Telegraph Diffusion Model for Restoring Texture Images with Multiplicative Noise
Multiplicative noise removal from texture images poses a significant challenge. Different from the diffusion equation-based filter, we consider the telegraph diffusion equation-based model, which can effectively preserve fine structures and edges for texture images. The fractional-order derivative is imposed due to its textural detail enhancing capability. We also introduce the gray level indicator, which fully considers the gray level information of multiplicative noise images, so that the model can effectively remove high level noise and protect the details of the structure. The well-posedness of the proposed fractional-order telegraph diffusion model is presented by applying the Schauder’s fixed-point theorem. To solve the model, we develop an iterative algorithm based on the discrete Fourier transform in the frequency domain. We give various numerical results on despeckling natural and real SAR images. The experiments demonstrate that the proposed method can remove multiplicative noise and preserve texture well