Well-posedness for a fourth order nonlinear equation related to image processing
نویسندگان
چکیده
منابع مشابه
Well-posedness for a fourth order nonlinear equation related to image processing
Using the entropy estimates in [14], we establish the global existence and uniqueness of solutions to a fourth order equation related to image processing. Some numerical results on the Lena image are also presented to show the effectiveness of the equation for noise removal.
متن کاملWell-Posedness for a Class of Fourth Order Diffusions for Image Processing
A number of image denoising models based on higher order parabolic partial differential equations (PDEs) have been proposed in an effort to overcome some of the problems attendant to second order methods such as the famous Perona-Malik model. However, there is little analysis of these equations to be found in the literature. In this paper, methods of maximal regularity are used to prove the exi...
متن کاملADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problem...
متن کاملWell-posedness and standing waves for the fourth-order non-linear Schrödinger-type equation
We consider the initial value problem for the fourth-order non-linear Schrödinger-type equation (4NLS) which describes the motion of an isolated vortex filament. In the first part of this note we review some recent results on the time local well-posedness of (4NLS) and give the alternative proof of those results. In the second part of this note we consider the stability of a standing wave solut...
متن کاملWell-posedness for a Higher-order Benjamin-ono Equation
In this paper we prove that the initial value problem associated to the following higher-order Benjamin-Ono equation ∂tv − bH∂ xv + a∂ xv = cv∂xv − d∂x(vH∂xv + H(v∂xv)), where x, t ∈ R, v is a real-valued function, H is the Hilbert transform, a ∈ R, b, c and d are positive constants, is locally well-posed for initial data v(0) = v0 ∈ H(R), s ≥ 2 or v0 ∈ H(R) ∩ L(R; xdx), k ∈ Z+, k ≥ 2.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis: Real World Applications
سال: 2014
ISSN: 1468-1218
DOI: 10.1016/j.nonrwa.2013.11.005