相关论文: Smoothed-TV Regularization for H\"older Continuous…
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $\alpha$-H\"older derivatives (for some $0<\alpha\leq 1$). The smooth approximation is given by means of an…
Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…
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…
We introduce a novel regulariser based on the natural vector field operations gradient, divergence, curl and shear. For suitable choices of the weighting parameters contained in our model it generalises well-known first- and second-order…
The 3-D total variation (3DTV) is a powerful regularization term, which encodes the local smoothness prior structure underlying a hyper-spectral image (HSI), for general HSI processing tasks. This term is calculated by assuming identical…
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)…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic…
We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
Total variation (TV) is a widely used regularizer for stabilizing the solution of ill-posed inverse problems. In this paper, we propose a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functional. Our…
Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we…
In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem involving the shape weighted perimeter and an additional term depending on a parameter. Based on recent works and 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…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
This article proposes a novel regularization method, named Geometric Spatio-Spectral Total Variation (GeoSSTV), for hyperspectral (HS) image denoising and destriping. HS images are inevitably affected by various types of noise due to the…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide…