相关论文: A Unified Framework for Total Variation Regularize…
When considering a general system of equations describing the space-time evolution (flow) of one or several variables, the problem of the optimization over a finite period of time of a measure of the state variable at the final time is a…
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
Total variation regularization has proven to be a valuable tool in the context of optimal control of differential equations. This is particularly attributed to the observation that TV-penalties often favor piecewise constant minimizers with…
Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation type functional…
This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
Total Variation (TV) and related extensions have been popular in image restoration due to their robust performance and wide applicability. While the original formulation is still relevant after two decades of extensive research, its…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
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)…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
This paper presents a convex optimization framework for eco-driving and vehicle energy management problems. We will first show that several types of eco-driving and vehicle energy management problems can be modelled using the same notions…
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and…
We propose an extended full-waveform inversion formulation that includes general convex constraints on the model. Though the full problem is highly nonconvex, the overarching optimization scheme arrives at geologically plausible results by…
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…
In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation…