Variational inference techniques are powerful methods for learning probabilistic models and provide significant advantages with respect to maximum likelihood (ML) or maximum a posteriori (MAP) approaches. Nevertheless they have not yet been fully exploited for image processing applications. In this paper we present a variational Bayes (VB) approach for image segmentation. We aim to show that VB...

In this paper, a novel variational model with strict convexity for removing multiplicative noise from images is proposed and studied. Firstly, by applying maximum likelihood estimation method and the Bayesian formulation, the variational model is derived. Then, we use an alternating minimization algorithm to find out the minimizer of the objective function, and prove the existence of the minimi...

This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange variational technique in the Riesz derivative sense and derives an approximate solitary wave solution. Our results witness that He’s variational iteration method was very efficient and powerful technique in finding the solution of the proposed equation. The basic idea described in this paper is...

Table of contents Chapter 1 ‘Incremental formulation of 3D/4D variational assimilation—an overview’ Chapter 2 ‘3D variational assimilation’ Chapter 3 ‘4D variational assimilation’ Chapter 4 ‘Background term’ Chapter 5 ‘Conventional observational constraints’ Chapter 6 ‘Satellite observational constraints’ Chapter 7 ‘Background, analysis and forecast errors’ Chapter 8 ‘Gravity-wave control’ Chap...

Table of contents Chapter 1 ‘Incremental formulation of 3D/4D variational assimilation—an overview’ Chapter 2 ‘3D variational assimilation’ Chapter 3 ‘4D variational assimilation’ Chapter 4 ‘Background term’ Chapter 5 ‘Conventional observational constraints’ Chapter 6 ‘Satellite observational constraints’ Chapter 7 ‘Background, analysis and forecast errors’ Chapter 8 ‘Gravity-wave control’ Chap...

Many problems in image analysis and computer vision involving boundaries and regions can be cast in a variational formulation. This means that m-surfaces, e.g. curves and surfaces, are determined as minimizers of functionals using e.g. the variational level set method. In this paper we consider such variational problems with constraints given by functionals. We use the geometric interpretation ...

We deal with initial-boundary value problems describing vertical vibrations of viscoelastic von Kármán-Donnell shells with a rigid inner obstacle. The short memory (Kelvin-Voigt) material is considered. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the penalization method.

The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini’s conditions and adhesion. The evolution of bonding field is described by a nonlin...

We discuss intrinsic aspects of Krupka’s approach to finite–order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite– order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite–order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present...

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational ...